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1

Ben Taher, R. y M. Rachidi. "The Near Subnormal Weighted Shift and Recursiveness". International Journal of Analysis 2013 (27 de marzo de 2013): 1–4. http://dx.doi.org/10.1155/2013/397262.

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We aim at studying the near subnormality of the unilateral weighted shifts, whose moment sequences are defined by linear recursive relations of finite order. Using the basic properties of recursive sequences, we provide a natural necessary condition, that ensure the near subnormality of this important class of weighted shifs. Some related new results are established; moreover, applications and consequences are presented; notably the notion of near subnormal completion weighted shift is implanted and explored.
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2

Szymanski, Waclaw. "Dilations and Subnormality". Proceedings of the American Mathematical Society 101, n.º 2 (octubre de 1987): 251. http://dx.doi.org/10.2307/2045991.

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3

Szymański, Wacław. "Dilations and subnormality". Proceedings of the American Mathematical Society 101, n.º 2 (1 de febrero de 1987): 251. http://dx.doi.org/10.1090/s0002-9939-1987-0902537-9.

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4

Insel, A. "Levels of Subnormality". Linear Algebra and its Applications 262, n.º 1-3 (1 de septiembre de 1997): 27–53. http://dx.doi.org/10.1016/s0024-3795(96)00466-1.

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5

Insel, Arnold J. "Levels of subnormality". Linear Algebra and its Applications 262 (septiembre de 1997): 27–53. http://dx.doi.org/10.1016/s0024-3795(97)80021-3.

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6

Kemoto, Nobuyuki. "Subnormality in ω12". Topology and its Applications 122, n.º 1-2 (julio de 2002): 287–96. http://dx.doi.org/10.1016/s0166-8641(01)00149-3.

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7

Demanze, Olivier. "On Subnormality and Formal Subnormality for Tuples of Unbounded Operators". Integral Equations and Operator Theory 46, n.º 3 (julio de 2003): 267–84. http://dx.doi.org/10.1007/s00020-002-1141-8.

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8

CRAWFORD, NICK. "SELF CONCEPT AND SUBNORMALITY". Journal of the Institute of Mental Subnormality (APEX) 4, n.º 1 (26 de agosto de 2009): 29–30. http://dx.doi.org/10.1111/j.1468-3156.1976.tb00219.x.

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9

Tizard, J. "PROGNOSIS AND MENTAL SUBNORMALITY". Developmental Medicine & Child Neurology 4, n.º 6 (12 de noviembre de 2008): 648–51. http://dx.doi.org/10.1111/j.1469-8749.1962.tb04162.x.

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10

Woolf, P. Grahame. "Subnormality Services in Sweden". Developmental Medicine & Child Neurology 12, n.º 4 (12 de noviembre de 2008): 525–30. http://dx.doi.org/10.1111/j.1469-8749.1970.tb01955.x.

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11

MIDWINTER, R. E. "MENTAL SUBNORMALITY IN BRISTOL". Journal of Intellectual Disability Research 16, n.º 1-2 (28 de junio de 2008): 48–56. http://dx.doi.org/10.1111/j.1365-2788.1972.tb01571.x.

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12

Curto, R. E., I. S. Hwang y W. Y. Lee. "Weak subnormality of operators". Archiv der Mathematik 79, n.º 5 (noviembre de 2002): 360–71. http://dx.doi.org/10.1007/pl00012458.

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13

Athavale, Ameer y Steen Pedersen. "Moment problems and subnormality". Journal of Mathematical Analysis and Applications 146, n.º 2 (marzo de 1990): 434–41. http://dx.doi.org/10.1016/0022-247x(90)90314-6.

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14

Cichoń, Dariusz y Jan Stochel. "Subnormality, Analyticity and Perturbations". Rocky Mountain Journal of Mathematics 37, n.º 6 (diciembre de 2007): 1831–69. http://dx.doi.org/10.1216/rmjm/1199649826.

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15

Rantakallio, Paula. "Social Class Differences in Mental Retardation and Subnormality". Scandinavian Journal of Social Medicine 15, n.º 2 (junio de 1987): 63–66. http://dx.doi.org/10.1177/140349488701500202.

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Social class and regional differences in mental retardation were studied in a birth cohort of 12000 children followed up until the age of 14. The incidence of severe mental retardation IQ<50 was significantly higher in farming families and in less developed areas, which is in agreement with the fact that a greater part of the population in these areas belong to social class IV and farmers. The obvious explanation for the higher incidence of severe mental retardation among farmers is an excess of older mothers in this group. In the group of severe mental retardation, paternal unemployment was also statistically, significantly more frequent than among the others. Mild mental retardation, IQ 50–70, was significantly higher in all classes other than I+II and mental subnormality, IQ 71–85 was higher in social classes III and IV. The other less favourable social conditions, which were statistically more frequent in the families of the mentally subnormal, were that: the father had died, was unemployed, on sick leave or receiveing a pension and the mother was not living at home, was unemployed, or was on sick leave or receiving a pension. The incidence of mental subnormality was significantly higher in more developed areas, in spite of the fact that the members of social class IV were less and those of classes I+II more numerous than elsewhere. One probable explanation for the higher incidence of mild mental retardation and mental subnormality in the lower social classes, is found in socio-familial factors, and, with regard to the excess of these conditions in urban areas, in either the difference in socio-cultural factors or in an eargerness to diagnose these conditions. When only the cases of mental retardation, for which no risk factor or aetiology was known, were considered, a statistically significant difference was only found in mild mental retardation and mental subnormality; the incidence of these conditions being higher in social class IV than in I+II.
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16

Adams, Gregory T., Nathan S. Feldman y Paul J. McGuire. "Tridiagonal reproducing kernels and subnormality". Journal of Operator Theory 70, n.º 2 (1 de octubre de 2013): 477–94. http://dx.doi.org/10.7900/jot.2011sep12.1942.

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17

DAMIAN, ERIKA y ANDREA LUCCHINI. "A PROBABILISTIC GENERALIZATION OF SUBNORMALITY". Journal of Algebra and Its Applications 04, n.º 03 (junio de 2005): 313–23. http://dx.doi.org/10.1142/s0219498805001204.

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A subnormal subgroup X of G has the following property: there exists a Dirichlet polynomial Q(s) with integer coefficients such that, for each t ∈ ℕ, Q(t) is the conditional probability that t random elements generate G given that they generate G together with the elements of X In this paper we analyze how far can a subgroup X be with this property from being a subnormal subgroup.
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18

MACKAY, D. N. "MENTAL SUBNORMALITY IN NORTHERN IRELAND". Journal of Intellectual Disability Research 15, n.º 1 (22 de julio de 2010): 12–19. http://dx.doi.org/10.1111/j.1365-2788.1971.tb01136.x.

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19

McDONALD, G. y D. N. MacKAY. "MENTAL SUBNORMALITY IN NORTHERN IRELAND". Journal of Intellectual Disability Research 22, n.º 2 (28 de junio de 2008): 83–89. http://dx.doi.org/10.1111/j.1365-2788.1978.tb00965.x.

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20

Stochel, Jan y F. H. Szafraniec. "Unbounded weighted shifts and subnormality". Integral Equations and Operator Theory 12, n.º 1 (enero de 1989): 146–53. http://dx.doi.org/10.1007/bf01199763.

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21

Doerk, K. y M. D. Pérez-Ramos. "A criterion for F-subnormality". Journal of Algebra 120, n.º 2 (febrero de 1989): 416–21. http://dx.doi.org/10.1016/0021-8693(89)90206-8.

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22

GOLDING, A. M. B. "ASCERTAINMENT OF SUBNORMALITY IN BEDFORDSHIRE". Journal of Intellectual Disability Research 12, n.º 1 (28 de junio de 2008): 81–83. http://dx.doi.org/10.1111/j.1365-2788.1968.tb00244.x.

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23

Yakivchik, Andrew N. "Subnormality in subspaces of products". Topology and its Applications 107, n.º 1-2 (octubre de 2000): 197–205. http://dx.doi.org/10.1016/s0166-8641(00)00093-6.

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24

Stochel, Jerzy Bartłomiej. "Subnormality and generalized commutation relations". Glasgow Mathematical Journal 30, n.º 3 (septiembre de 1988): 259–62. http://dx.doi.org/10.1017/s0017089500007333.

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In the theory of Hilbert space operators an important question is whether an operator is subnormal [3], [4], [7], [8]. A densely defined linear operator S in a complex Hilbert space H is subnormal if there exists a normal operator N in a complex Hilbert space K ⊃ H such that S ⊂ N.
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25

Spencer, D. A. "ROLE OF MEDICAL SPECIALIST IN SUBNORMALITY". Journal of the Institute of Mental Subnormality (APEX) 3, n.º 4 (26 de agosto de 2009): 32–33. http://dx.doi.org/10.1111/j.1468-3156.1976.tb00199.x.

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26

SCOTT, ANNE y FAULKNER L. MACKENZIE. "Further education: in a subnormality hospital". Journal of the Institute of Mental Subnormality (APEX) 4, n.º 1 (26 de agosto de 2009): 20–23. http://dx.doi.org/10.1111/j.1468-3156.1976.tb00213.x.

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27

LEYS, DUNCAN. "The Mental Health Act and Subnormality". Developmental Medicine & Child Neurology 5, n.º 6 (12 de noviembre de 2008): 656–57. http://dx.doi.org/10.1111/j.1469-8749.1963.tb10744.x.

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28

King, Walter C. y Nina Morton-Gore. "The Nadi Reaction and Mental Subnormality". Developmental Medicine & Child Neurology 8, n.º 3 (12 de noviembre de 2008): 327–29. http://dx.doi.org/10.1111/j.1469-8749.1966.tb01754.x.

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29

JABLONSKI, ZENON J. y JAN STOCHEL. "SUBNORMALITY AND OPERATOR MULTIDIMENSIONAL MOMENT PROBLEMS". Journal of the London Mathematical Society 71, n.º 02 (abril de 2005): 438–66. http://dx.doi.org/10.1112/s0024610705006289.

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30

Cocke, W. "Subnormality and the Chermak–Delgado lattice". Journal of Algebra and Its Applications 19, n.º 08 (13 de julio de 2019): 2050141. http://dx.doi.org/10.1142/s0219498820501418.

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The Chermak–Delgado lattice of a finite group [Formula: see text] is a sublattice of the subgroup lattice of [Formula: see text] that has attracted interest since its discovery. In this paper, we show that every subgroup of [Formula: see text] in the Chermak–Delgado lattice is subnormal in [Formula: see text] with subnormal depth bounded by both the depth and height function of the Chermak–Delgado lattice; we provide a nontrivial example showing that our bounds are sharp. We also show that determining whether a given subgroup [Formula: see text] is in the Chermak–Delgado lattice can be decided by examining only those subgroups of [Formula: see text] that are comparable with [Formula: see text].
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31

Kappe, Luise-Charlotte y Gunnar Traustason. "Subnormality conditions in non-torsion groups". Bulletin of the Australian Mathematical Society 59, n.º 3 (junio de 1999): 459–65. http://dx.doi.org/10.1017/s0004972700033141.

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According to results of Heineken and Stadelmann, a non-torsion group is a 2-Baer group if and only if it is 2-Engel, and it has all subgroups 2-subnormal if and only if it is nilpotent of class 2. We extend some of these results to values of n greater than 2. Any non-torsion group which is an n-Baer group is an n-Engel group. The converse holds for n = 3, and for all n in the case of metabelian groups. A non-torsion group without involutions having all subgroups 3-subnormal has nilpotency class 4, and this bound is sharp.
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32

Szafraniec, Franciszek Hugon. "Subnormality in the Quantum Harmonic Oscillator". Communications in Mathematical Physics 210, n.º 2 (1 de marzo de 2000): 323–34. http://dx.doi.org/10.1007/s002200050782.

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33

Casolo, Carlo. "Subnormality in factorizable finite soluble groups". Archiv der Mathematik 57, n.º 1 (julio de 1991): 12–13. http://dx.doi.org/10.1007/bf01200032.

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34

Cowen, Carl C. y Thomas L. Kriete. "Subnormality and composition operators on H2". Journal of Functional Analysis 81, n.º 2 (diciembre de 1988): 298–319. http://dx.doi.org/10.1016/0022-1236(88)90102-4.

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35

Ragusa, Letizia, Corrado Romano, Pinella Failla, Caterina Proto y Fabio Colabucci. "Growth hormone subnormality in down syndrome". American Journal of Medical Genetics 43, n.º 5 (15 de julio de 1992): 894–95. http://dx.doi.org/10.1002/ajmg.1320430529.

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36

Ferrara, Maria y Marco Trombetti. "σ-Subnormality in locally finite groups". Journal of Algebra 614 (enero de 2023): 867–97. http://dx.doi.org/10.1016/j.jalgebra.2022.10.013.

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37

Curto, Raúl E., Yiu T. Poon y Jasang Yoon. "Subnormality of Bergman-like weighted shifts". Journal of Mathematical Analysis and Applications 308, n.º 1 (agosto de 2005): 334–42. http://dx.doi.org/10.1016/j.jmaa.2005.01.028.

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38

Das, Dhruba y Hemanta K. Baruah. "Imprecise Vector: The Case of Subnormality". National Academy Science Letters 40, n.º 6 (13 de noviembre de 2017): 455–60. http://dx.doi.org/10.1007/s40009-017-0601-2.

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39

Cowen, Carl C. "Transferring subnormality of adjoint composition operators". Integral Equations and Operator Theory 15, n.º 1 (enero de 1992): 167–71. http://dx.doi.org/10.1007/bf01193772.

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40

Jahan, Iffat, Naseem Ajmal y Bijan Davvaz. "Subnormality and Theory of L-subgroups". European Journal of Pure and Applied Mathematics 15, n.º 4 (31 de octubre de 2022): 2086–115. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4548.

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The main focus in this work is to establish that L-group theory, which uses the language of functions instead of formal set theoretic language, is capable of capturing most of the refined ideas and concepts of classical group theory. We demonstrate this by extending the notion of subnormality to the L-setting and investigating its properties. We develop a mechanism to tackle the join problem of subnormal L-subgroups. The conjugate L-subgroup as is defined in our previous paper [4] has been used to formulate the concept of normal closure and normal closure series of an L-subgroup which, in turn, is used to define subnormal L-subgroups. Further, the concept of subnormal series has been introduced in L-setting and utilized to establish the subnor-mality of L-subgroups. Also, several results pertaining to the notion of subnormality have been established. Lastly, the level subset characterization of a subnormal L-subgroup is provided after developing a necessary mechanism. Finally, we establish that every subgroup of a nilpotent L-group is subnormal. In fact, it has been exhibited through this work that L-group theory presents a modernized approach to study classical group theory.
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41

Khosravi, H. "Finite Groups with a Subnormality Condition". Siberian Mathematical Journal 63, n.º 6 (noviembre de 2022): 1223–30. http://dx.doi.org/10.1134/s0037446622060180.

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42

JUNG, IL BONG, SUN HYUN PARK y JAN STOCHEL. "L(n)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY". Journal of the Australian Mathematical Society 88, n.º 2 (abril de 2010): 193–203. http://dx.doi.org/10.1017/s1446788710000091.

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AbstractA new notion of L(n)-hyponormality is introduced in order to provide a bridge between subnormality and paranormality, two concepts which have received considerable attention from operator theorists since the 1950s. Criteria for L(n)-hyponormality are given. Relationships to other notions of hyponormality are discussed in the context of weighted shift and composition operators.
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43

Hwang, In Sung, In Hyoun Kim y Su in Kim. "Weak subnormality of infinite 4-banded matrices". Operators and Matrices, n.º 1 (2021): 117–25. http://dx.doi.org/10.7153/oam-2021-15-08.

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44

Ballester-Bolinches, A., S. F. Kamornikov y X. Yi. "On σ-subnormality criteria in finite groups". Journal of Pure and Applied Algebra 226, n.º 2 (febrero de 2022): 106822. http://dx.doi.org/10.1016/j.jpaa.2021.106822.

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45

Lee, Sang Hoon, Woo Young Lee y Jasang Yoon. "Subnormality of Powers of Multivariable Weighted Shifts". Journal of Function Spaces 2020 (27 de noviembre de 2020): 1–11. http://dx.doi.org/10.1155/2020/5678795.

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Given a pair T ≡ T 1 , T 2 of commuting subnormal Hilbert space operators, the Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for the existence of a commuting pair N ≡ N 1 , N 2 of normal extensions of T 1 and T 2 ; in other words, T is a subnormal pair. The LPCS is a longstanding open problem in the operator theory. In this paper, we consider the LPCS of a class of powers of 2 -variable weighted shifts. Our main theorem states that if a “corner” of a 2-variable weighted shift T = W α , β ≔ T 1 , T 2 is subnormal, then T is subnormal if and only if a power T m , n ≔ T 1 m , T 2 n is subnormal for some m , n ≥ 1 . As a corollary, we have that if T is a 2-variable weighted shift having a tensor core or a diagonal core, then T is subnormal if and only if a power of T is subnormal.
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46

Mahendra, B. "SUBNORMALITY REVISITED IN EARLY 19TH CENTURY FRANCE". Journal of Intellectual Disability Research 29, n.º 4 (28 de junio de 2008): 391–401. http://dx.doi.org/10.1111/j.1365-2788.1985.tb00365.x.

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47

Jabłoński, Zenon J. "Complete hyperexpansivity, subnormality and inverted boundedness conditions". Integral Equations and Operator Theory 44, n.º 3 (septiembre de 2002): 316–36. http://dx.doi.org/10.1007/bf01212036.

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48

Yajima, Yukinobu. "Subnormality of X × κ and Σ-products". Topology and its Applications 54, n.º 1-3 (diciembre de 1993): 111–22. http://dx.doi.org/10.1016/0166-8641(93)90055-i.

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49

Curto, Raúl E., In Sung Hwang y Woo Young Lee. "Hyponormality and subnormality of block Toeplitz operators". Advances in Mathematics 230, n.º 4-6 (julio de 2012): 2094–151. http://dx.doi.org/10.1016/j.aim.2012.04.019.

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50

Kamornikov, S. F. "Permutability of subgroups and $$\mathfrak{F}$$ -subnormality". Siberian Mathematical Journal 37, n.º 5 (septiembre de 1996): 936–49. http://dx.doi.org/10.1007/bf02110725.

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