Relevant bibliographies by topics / Commutant Lifting Theorem

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Academic literature on the topic 'Commutant Lifting Theorem'

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Published: 6 September 2023

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Journal articles on the topic "Commutant Lifting Theorem"

1

Bercovici, Hari, Ciprian Foias, and Allen Tannenbaum. "A spectral commutant lifting theorem." Transactions of the American Mathematical Society 325, no. 2 (February 1, 1991): 741–63. http://dx.doi.org/10.1090/s0002-9947-1991-1000144-9.

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2

Szehr, Oleg, and Rachid Zarouf. "Interpolation without commutants." Journal of Operator Theory 84, no. 1 (May 15, 2020): 239–56. http://dx.doi.org/10.7900/jot.2019may21.2264.

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We introduce a ``dual-space approach'' to mixed Nevanlinna--Pick Carath\'eodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting one of D. Sarason and B. Nagy-C. Foia\c{s}. We compute the norm of the minimal interpolant in X by a version of the Hahn-Banach theorem, which we use to extend functionals defined on a subspace of kernels without increasing their norm. This functional extension lemma plays a similar role as Sarason's commutant lifting theorem but it only involves the predual of X and no Hilbert space structure is needed. As an example, we present the respective Pick-type interpolation theorems for Beurling-Sobolev spaces.
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3

Popescu, Gelu. "Andô dilations and inequalities on non-commutative domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 6 (July 6, 2018): 1239–67. http://dx.doi.org/10.1017/s030821051800015x.

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We obtain intertwining dilation theorems for non-commutative regular domains 𝒟f and non-commutative varieties 𝒱J in B(𝓗)n, which generalize Sarason and Szőkefalvi-Nagy and Foiaş's commutant lifting theorem for commuting contractions. We present several applications including a new proof for the commutant lifting theorem for pure elements in the domain 𝒟f (respectively, variety 𝒱J ) as well as a Schur-type representation for the unit ball of the Hardy algebra associated with the variety 𝒱J. We provide Andô-type dilations and inequalities for bi-domains 𝒟f ×c 𝒟g consisting of all pairs (X,Y ) of tuples X := (X1,…, Xn1) ∊ 𝒟f and Y := (Y1,…, Yn2) ∊ 𝒟g that commute, i.e. each entry of X commutes with each entry of Y . The results are new, even when n1 = n2 = 1. In this particular case, we obtain extensions of Andô's results and Agler and McCarthy's inequality for commuting contractions to larger classes of commuting operators. All the results are extended to bi-varieties 𝒱J1×c 𝒱J2, where 𝒱J1 and 𝒱J2 are non-commutative varieties generated by weak-operator-topology-closed two-sided ideals in non-commutative Hardy algebras. The commutative case and the matrix case when n1 = n2 = 1 are also discussed.
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Popescu, Gelu. "!COMMUTANT LIFTING, TENSOR ALGEBRAS, AND FUNCTIONAL CALCULUS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (June 2001): 389–406. http://dx.doi.org/10.1017/s0013091598001059.

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AbstractA non-commutative multivariable analogue of Parrott’s generalization of the Sz.-Nagy–Foia\c{s} commutant lifting theorem is obtained. This yields Tomita-type commutant results and interpolation theorems (e.g. Sarason, Nevanlinna–Pick, Carathéodory) for $F_n^\infty\,\bar{\otimes}\,\M$, the weakly-closed algebra generated by the spatial tensor product of the non-commutative analytic Toeplitz algebra $F_n^\infty$ and an arbitrary von Neumann algebra $\M$. In particular, we obtain interpolation theorems for bounded analytic functions from the open unit ball of $\mathbb{C}^n$ into a von Neumann algebra.A variant of the non-commutative Poisson transform is used to extend the von Neumann inequality to tensor algebras, and to provide a generalization of the functional calculus for contractive sequences of operators on Hilbert spaces. Commutative versions of these results are also considered.AMS 2000 Mathematics subject classification: Primary 47L25; 47A57; 47A60. Secondary 30E05
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Ball, J. A., W. S. Li, D. Timotin, and T. T. Trent. "A commutant lifting theorem on the polydisc." Indiana University Mathematics Journal 48, no. 2 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1708.

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Sultanic, Saida. "Commutant Lifting Theorem for the Bergman Space." Integral Equations and Operator Theory 55, no. 4 (May 3, 2006): 573–95. http://dx.doi.org/10.1007/s00020-006-1442-4.

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7

Gu, Caixing. "On causality in commutant lifting theorem. I." Integral Equations and Operator Theory 16, no. 1 (March 1993): 82–97. http://dx.doi.org/10.1007/bf01196603.

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Timotin, Dan. "Completions of matrices and the commutant lifting theorem." Journal of Functional Analysis 104, no. 2 (March 1992): 291–98. http://dx.doi.org/10.1016/0022-1236(92)90002-z.

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9

Freydin, Boris. "Commutant lifting theorem and interpolation in discrete nest algebras." Integral Equations and Operator Theory 29, no. 2 (June 1997): 211–30. http://dx.doi.org/10.1007/bf01191431.

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10

Timotin, Dan. "The weighted commutant lifting theorem in the coupling approach." Integral Equations and Operator Theory 42, no. 4 (December 2002): 493–97. http://dx.doi.org/10.1007/bf01270926.

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Dissertations / Theses on the topic "Commutant Lifting Theorem"

1

Mandal, Samir Ch. "Dilation Theory of Contractions and Nevanlinna-Pick Interpolation Problem." Thesis, 2014. http://etd.iisc.ac.in/handle/2005/4110.

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In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's inequality'. Next we give a complete description of the dilation of a pure contraction. We also discuss Ando's proof of the existence of a unitary dilation of a pair of commuting contractions and give an example to show that this result does not hold, in general, for more than two commuting contractions. Then we describe and prove the `commutant lifting theorem' and lastly, we use this theorem to prove the operator valued `Nevanlinna-Pick interpolation problem'.
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Books on the topic "Commutant Lifting Theorem"

1

Foiaş, Ciprian. The commutant lifting approach to interpolation problems. Basel: Birkhäuser, 1990.

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2

Ciprian, Foiaş, ed. Metric constrained interpolation, commutant lifting, and systems. Basel: Birkhäuser, 1998.

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3

The Commutant Lifting Approach to Interpolation Problems. Springer, 2013.

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Book chapters on the topic "Commutant Lifting Theorem"

1

Foias, Ciprian, and Arthur E. Frazho. "The Commutant Lifting Theorem." In The Commutant Lifting Approach to Interpolation Problems, 153–90. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7712-1_7.

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Foias, C., A. E. Frazho, I. Gohberg, and M. A. Kaashoek. "Proofs Using the Commutant Lifting Theorem." In Metric Constrained Interpolation, Commutant Lifting and Systems, 51–72. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8791-5_3.

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3

Foias, C., A. E. Frazho, I. Gohberg, and M. A. Kaashoek. "A General Completion Theorem." In Metric Constrained Interpolation, Commutant Lifting and Systems, 423–67. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8791-5_13.

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Foias, Ciprian, and Arthur E. Frazho. "Geometric Applications of the Commutant Lifting Theorem." In The Commutant Lifting Approach to Interpolation Problems, 191–232. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7712-1_8.

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5

Gu, Caixing. "On a Nonlinear Causal Commutant Lifting Theorem." In Operator Theory and Interpolation, 195–212. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8422-8_9.

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6

Foias, Ciprian, and Arthur E. Frazho. "Inverse Scattering Algorithms for the Commutant Lifting Theorem." In The Commutant Lifting Approach to Interpolation Problems, 367–426. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7712-1_13.

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7

Foias, C., A. E. Frazho, I. Gohberg, and M. A. Kaashoek. "Applications of the Three Chains Completion Theorem to Interpolation." In Metric Constrained Interpolation, Commutant Lifting and Systems, 469–95. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8791-5_14.

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8

Bruzual, Ramon, and Marisela Dominguez. "A Proof of the Continuous Commutant Lifting Theorem." In Operator Theory and Related Topics, 83–89. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8413-6_6.

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9

Gadidov, Radu. "On the Commutant Lifting Theorem and Hankel Operators." In Algebraic Methods in Operator Theory, 3–9. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0255-4_1.

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Dijksma, Aad, Michael Dritschel, Stefania Marcantognini, and Henk de Snoo. "The Commutant Lifting Theorem for Contractions on Kreĭn Spaces." In Operator Extensions, Interpolation of Functions and Related Topics, 65–83. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8575-1_4.

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Conference papers on the topic "Commutant Lifting Theorem"

1

Ambrozie, Calin, and Jörg Eschmeier. "A commutant lifting theorem on analytic polyhedra." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-7.

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