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On the Fredholm theory of multipliers


Author: Pietro Aiena
Journal: Proc. Amer. Math. Soc. 120 (1994), 89-96
MSC: Primary 46J05; Secondary 46H30, 47A53, 47B48
MathSciNet review: 1145939
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Abstract: Multipliers that are Fredholm operators on certain commutative semisimple Banach algebras may be characterized by means of a quotient algebra of multipliers. Some spectral properties of multipliers of these algebras are considered


References [Enhancements On Off] (What's this?)

  • [1] P. Aiena, Riesz multipliers on commutative semi-simple Banach algebras, Arch. Math. (Basel) 50 (1990), 293-303. MR 1037620 (91e:46064)
  • [2] -, Multipliers on Banach algebras with orthogonal basis, Boll. Un. Mat. Ital. (7) 5-B (1991), 240-256.
  • [3] C. A. Akemann, Some mapping properties of the group algebra of a compact group, Pacific J. Math. 22 (1967), 1-8. MR 0212587 (35:3458)
  • [4] B. A. Barnes, Inverse closed subalgebras and Fredholm theory, Proc. Roy. Irish. Acad. Sect. A 83 (1983), 217-224. MR 736497 (85c:46042)
  • [5] B. A. Barnes, G. J. Murphy, M. R. Smyth, and T. T. West, Riesz and Fredholm theory in Banach algebras, Research Notes in Math., vol. 67, Pitman, London, 1982.
  • [6] F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, Berlin, Heidelberg, and New York, 1973. MR 0423029 (54:11013)
  • [7] S. R. Caradus, W. E. Pfaffenberger, and B. Yood, Calkin algebra and algebras of operators on Banach spaces, Dekker, New York, 1974. MR 0415345 (54:3434)
  • [8] H. Heuser, Functional analysis, Wiley, New York, 1982. MR 640429 (83m:46001)
  • [9] T. Husain and S. Watson, Topological algebras with orthogonal Schauder basis, Pacific J. Math. 91 (1980), 339-347. MR 615682 (82h:46064)
  • [10] H. Kamowitz, On compact multipliers of Banach algebras, Proc. Amer. Math. Soc. 81 (1981), 79-80. MR 589140 (81j:47020)
  • [11] I. Kaplansky, Dual rings, Ann. of Math. (2) 49 (1948), 689-701. MR 0025452 (10:7b)
  • [12] R. Larsen, An introduction to the theory of multipliers, Springer-Verlag, Berlin, Heidelberg, and New York, 1971. MR 0435738 (55:8695)
  • [13] G. E. Silov, On decomposition of a commutative normed ring in a direct sum of ideals, Mat. Sb. 32 (1953), 353-364. MR 0054177 (14:884b)
  • [14] J. K.Wang, Multipliers of commutative Banach algebras, Pacific J. Math. 11 (1961), 1131-1149. MR 0138014 (25:1462)
  • [15] J. G. Wendel, On isometric isomorphisms of group algebras, Pacific J. Math. 1 (1951), 305-311. MR 0049910 (14:246b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1145939-4
Keywords: Multipliers on commutative semisimple Banach algebras, Fredholm theory
Article copyright: © Copyright 1994 American Mathematical Society