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Nasr-Isfahani, R. "Fixed point characterization of left amenable Lau algebras." International Journal of Mathematics and Mathematical Sciences 2004, no. 62 (2004): 3333–38. http://dx.doi.org/10.1155/s0161171204310446.
The present paper deals with the concept of left amenability for a wide range of Banach algebras known as Lau algebras. It gives a fixed point property characterizing left amenable Lau algebras𝒜in terms of left Banach𝒜-modules. It also offers an application of this result to some Lau algebras related to a locally compact groupG, such as the Eymard-Fourier algebraA(G), the Fourier-Stieltjes algebraB(G), the group algebraL1(G), and the measure algebraM(G). In particular, it presents some equivalent statements which characterize amenability of locally compact groups.
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Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.
Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.
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Yoon Yang, Seo, Abasalt Bodaghi, and Kamel Ariffin Mohd Atan. "Approximate Cubic ∗-Derivations on Banach ∗-Algebras." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/684179.
Ebadian, A., and A. Jabbari. "ГИПЕРТАУБЕРОВЫ АЛГЕБРЫ, ОПРЕДЕЛЕННЫЕ ГОМОМОРФИЗМОМ БАНАХОВОЙ АЛГЕБРЫ." Вестник КРАУНЦ. Физико-математические науки, no. 1 (May 4, 2019): 18–28. http://dx.doi.org/10.26117/2079-6641-2019-26-1-18-28.
Let A and B be Banach algebras and T: B→A be a continuous homomorphism. We consider left multipliers from A×TB into its the first dual i.e., A*×B* and we show that A×TB is a hyper-Tauberian algebra if and only if A and B are hyper-Tauberian algebras. Пусть A и B – банаховы алгебры, а T: B→A – непрерывный гомоморфизм. Мы рассматриваем левые мультипликаторы из A×TB в его первое двойственное, т.е. A*×B*, и показываем, что A×TB является гипертауберовой алгеброй тогда и только тогда, когда A и B являются гипертауберовыми алгебрами.
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Ludkowski, Sergey Victor. "Algebras of Vector Functions over Normed Fields." Inventions 7, no. 4 (November 14, 2022): 102. http://dx.doi.org/10.3390/inventions7040102.
This article is devoted to study of vector functions in Banach algebras and Banach spaces over normed fields. A structure of their Banach algebras is investigated. Banach algebras of vector functions with values in ∗-algebras, finely regular algebras, B∗-algebras, and operator algebras are scrutinized. An approximation of vector functions is investigated. The realizations of these algebras by operator algebras are studied.
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Srivastava, Neeraj, S. Bhattacharya, and S. N. Lal. "2-normed algebras-II." Publications de l'Institut Math?matique (Belgrade) 90, no. 104 (2011): 135–43. http://dx.doi.org/10.2298/pim1104135s.
In the first part of the paper [5], we gave a new definition of real or complex 2-normed algebras and 2-Banach algebras. Here we give two examples which establish that not all 2-normed algebras are normable and a 2-Banach algebra need not be a 2-Banach space. We conclude by deriving a new and interesting spectral radius formula for 1-Banach algebras from the basic properties of 2-Banach algebras and thus vindicating our definitions of 2-normed and 2-Banach algebras given in [5].
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DIXON, P. G. "Graded Banach algebras associated with varieties of Banach algebras." Mathematical Proceedings of the Cambridge Philosophical Society 135, no. 3 (November 2003): 469–79. http://dx.doi.org/10.1017/s0305004103006972.
Schmitt, Lothar M. "Quotients of local Banach algebras are local Banach algebras." Publications of the Research Institute for Mathematical Sciences 27, no. 6 (1991): 837–43. http://dx.doi.org/10.2977/prims/1195169002.
BATKUNDE, HARMANUS, and Elvinus R. Persulessy. "ALJABAR-C* DAN SIFATNYA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 6, no. 1 (March 1, 2012): 19–22. http://dx.doi.org/10.30598/barekengvol6iss1pp19-22.
These notes in this paper form an introductory of C*-algebras and its properties. Some results on more general Banach algebras and C*-algebras, are included. We shall prove and discuss basic properties of Banach Algebras, C*-algebras, and commutative C*-algebras. We will also give important examples for Banach Algebras, C*-algebras, and commutative C*-algebras.
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Allan, Graham R., and Theodore W. Palmer. "Banach Algebras and the General Theory of Algebras. Volume 1: Algebras and Banach Algebras." Mathematical Gazette 80, no. 489 (November 1996): 635. http://dx.doi.org/10.2307/3618560.
Chapter 1 defines the notion of a unitary Banach algebra, and gives various examples. The inheritance of the unitary property of quotients and subalgebras is investigated, the main result being that the class of unitary Banach algebras is exactly the class of quotients of discrete group algebras. One problem that is discussed is whether a unitary subalgebra needs to inherit the unit element. Chapter 2 gives several other characterisations of unitary Banach algebras among norm-unital Banach algebras, in particular by conditions on the numerical range. The topological properties of the unitary Banach algebra are also discussed. Chapter 3 deals with isometric isomorphisms of unitary Banach algebras. In particular it is shown that, for groups G1 and G2, and A a norm-unital Banach algebra with connected unitary group, or a unital C*-algebra, the existence of an isometric isomorphism from l1 (G1, A) onto ll (G2, A) implies that G1 and G2 are isomorphic. If A is commutative then these two results can be generalised to be case of locally compact abelian groups G1 and G2, and the Banach algebras L1(G1, A) and L1 (G2, A).
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Daws, Matthew David Peter. "Banach algebras of operators." Thesis, University of Leeds, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414151.
Gourdeau, Frederic Marcel. "Amenability of Banach algebras." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305500.
Heath, Matthew J. "Bounded derivations from Banach algebras." Thesis, University of Nottingham, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.519425.
Knapper, Andrew. "Derivations on certain banach algebras." Thesis, University of Birmingham, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368411.
Feinstein, Joel Francis. "Derivations from Banach function algebras." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329058.
This thesis is devoted to the study of various properties of Banach function algebras. We are particularly interested in the study of antisymmetric decompositions for uniform algebras and regularity of Banach function algebras. We are also interested in the study of Swiss cheese sets, essential uniform algebras and characterisations of C(X) among its subalgebras. The maximal antisymmetric decomposition for uniform algebras is a generalisation of the celebrated Stone-Weierstrass theorem and it is a powerful tool in the study of uniform algebras. However, in the literature, not much attention has been paid to the study of closed antisymmetric subsets. In Section 1.7 we give a characterisation of all the closed antisymmetric subsets for the disc algebra on the unit circle, and we use this characterisation to give a new proof of Wermer’s maximality theorem. Then in Section 4.1 we give characterisations of all the closed antisymmetric subsets for normal uniform algebras on the unit interval or the unit circle. The two types of regularity points, the R-point and the point of regularity, are important concepts in the study of regularity of Banach function algebras. In Section 3.2 we construct two examples of compact plane sets X, such that R(X) has either one R-point while having no points of regularity, or R(X) has one point of continuity while having no R-points. There are the first known examples of natural uniform algebras in the literature which show that R-points and points of continuity can be different. We then use properties of regularity points to study R(X) which is not regular while having no non-trivial Jensen measures. We also use properties of regularity points in Section 4.2 to study small exceptional sets for uniform algebras. In Chapter 2 we study Swiss cheese sets. Our approach is to regard Swiss cheese sets “abstractly”: we study the family of sequences of pairs of numbers, where the numbers represent the centre and radius of discs in the complex plane. We then give a natural topology on the space of abstract Swiss cheeses and give topological proofs of various classicalisation theorems. It is standard that the study of general uniform algebras can be reduced to the study of essential uniform algebras. In Chapter 5 we study methods to construct essential uniform algebras. In particular, we continue to study the method introduced in [26] to show that some more properties are inherited by the constructed essential uniform algebra from the original one. We note that the material in Chapter 2 is joint work with J. Feinstein and S. Morley and is published in [28, 27]. The material in Chapter 3 is joint work with J. Feinstein and is published in [32]. Section 4.2 contains joint work with J. Feinstein.
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Mudau, Leonard Gumani. "Zero divisors in banach algebras." Thesis, University of Limpopo (Medunsa Campus), 2010. http://hdl.handle.net/10386/632.
Choi, Yemon. "Cohomology of commutative Banach algebras and l¹-semigroup algebras." Thesis, University of Newcastle Upon Tyne, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427291.
Schick, G. J. "Spectrally bounded operators on Banach algebras." Thesis, Queen's University Belfast, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390862.
International Conference on Banach Algebras (19th 2009 Stefan Banach International Mathematical Center). Banach algebras 2009. Edited by Loy Richard J, Runde Volker, Sołtysiak Andrzej, Stefan Banach International Mathematical Center, and Instytut Matematyczny (Polska Akademia Nauk). Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2010.
Müller, Vladimir. "Banach Algebras." In Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, 1–79. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7788-6_1.
Douglas, Ronald G. "Banach Algebras." In Graduate Texts in Mathematics, 30–57. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1656-8_2.
Kutateladze, S. S. "Banach Algebras." In Fundamentals of Functional Analysis, 213–35. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8755-6_11.
Bogachev, Vladimir I., and Oleg G. Smolyanov. "Banach Algebras." In Real and Functional Analysis, 483–510. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38219-3_11.
Deitmar, Anton, and Siegfried Echterhoff. "Banach Algebras." In Principles of Harmonic Analysis, 37–60. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05792-7_2.
Dales, H. G., and A. Ya Helemskii. "Banach algebras." In Lecture Notes in Mathematics, 51–154. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0100203.
Bowers, Adam, and Nigel J. Kalton. "Banach Algebras." In An Introductory Course in Functional Analysis, 181–206. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1945-1_8.
Pohl, Volker, and Holger Boche. "Banach Algebras." In Foundations in Signal Processing, Communications and Networking, 51–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03639-2_3.
Roch, Steffen, Pedro A. Santos, and Bernd Silbermann. "Banach algebras." In Non-commutative Gelfand Theories, 3–61. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-183-7_1.
Jarosz, Krzysztof. "Wiesław Żelazko, topological algebras, Banach algebras." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-1.
Laustsen, Niels Jakob, and Richard J. Loy. "Closed ideals in the Banach algebra of operators on a Banach space." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-20.
BASSEY, U. N. "ON COMPACT ELEMENTS OF BANACH ALGEBRAS." In Proceedings of the Fourth International Workshop. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773241_0020.
González, Manuel. "Banach spaces with small Calkin algebras." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-10.
Moslehian, Mohammad Sal. "On (Co)homology of triangular Banach algebras." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-22.
PLAKSA, S. A. "HARMONIC COMMUTATIVE BANACH ALGEBRAS AND SPATIAL POTENTIAL FIELDS." In Proceedings of the Conference Satellite to ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812778833_0015.
PALACIOS, ÁNGEL RODRÍGUEZ. "ABSOLUTE-VALUED ALGEBRAS, AND ABSOLUTE-VALUABLE BANACH SPACES." In Proceedings of the First International School. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702371_0005.
Allan, Graham R. "Elements of finite closed descent in Banach and Fréchet algebras." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-6.
Gürdal, M., U. Yamancı, and S. Saltan. "Generators of certain function Banach algebras and related questions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756301.
Keyl, Michael. "Quantum control in infinite dimensions and Banach-Lie algebras." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9029317.
