Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Banach algebras which are not Wedderburnian


Author: Bertram Yood
Journal: Proc. Amer. Math. Soc. 118 (1993), 1125-1130
MSC: Primary 46H10
DOI: https://doi.org/10.1090/S0002-9939-1993-1150660-1
MathSciNet review: 1150660
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a Banach algebra with radical $ R$. In 1951 Feldman exhibited an example in which it is impossible to find a closed subalgebra $ K$ of $ A$ such that $ A = K \oplus R$. We provide other examples. Feldman's algebra is commutative, but these examples are, in general, not commutative.


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

  • [1] W. G. Bade and P. C. Curtis, Homomorphisms of commutative Banach algebras, Amer. J. Math. 82 (1960), 589-608. MR 0117577 (22:8354)
  • [2] -, The Wedderburn decomposition of commutative Banach algebras, Amer. J. Math. 82 (1960), 851-861. MR 0123200 (23:A529)
  • [3] J. B. Conway, The theory of subnormal operators, Math. Surveys Monographs, vol. 36, Amer. Math. Soc., Providence, RI, 1991. MR 1112128 (92h:47026)
  • [4] C. Feldman, The Wedderburn principal theorem in Banach algebras, Proc. Amer. Math. Soc. 2 (1951), 771-777. MR 0044042 (13:361b)
  • [5] G. Glaeser, Étude de certaines algèbres Taylorienne, J. Analyse Math. 6 (1958), 1-124. MR 0101294 (21:107)
  • [6] E. Hewitt and K. A. Ross, Abstract harmonic analysis, vol. I, Springer-Verlag, New York, 1963. MR 551496 (81k:43001)
  • [7] I. Kaplansky, Dual rings, Ann. of Math. (2) 49 (1948), 689-701. MR 0025452 (10:7b)
  • [8] J. R. Ringrose, Compact non-self-adjoint operators, Van Nostrand Reinhold, New York. 1971.
  • [9] R. Schatten, Norm ideals of complete by continuous operators, Springer-Verlag, Berlin, 1960. MR 0119112 (22:9878)
  • [10] A. E. Taylor, Introduction to functional analysis, Wiley, New York, 1958. MR 0098966 (20:5411)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H10

Retrieve articles in all journals with MSC: 46H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1150660-1
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society