Download PDF - Symmetric Banach *-algebras: invariance of spectrumAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Symmetric Banach *-algebras: invariance of spectrum

Authors 1

Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A.

Abstract

Let A be a Banach *-algebra which is a subalgebra of a Banach algebra B. In this paper, assuming that A is symmetric, various conditions are given which imply that A is inverse closed in B.

Keywords

ENG
*-inverse closed, inverse closed, symmetric Banach *-algebra

Bibliography

  1. [B1] B. Barnes, The properties *-regularity and uniqueness of C*-norm in a general *-algebra, Trans. Amer. Math. Soc. 279 (1983), 841-859.
  2. [B2] B. Barnes, The spectrum of integral operators on Lebesgue space, J. Operator Theory 18 (1987), 115-132.
  3. [B3] B. Barnes, A note on invariance of spectrum for symmetric Banach *-algebras, Proc. Amer. Math. Soc. 126 (1998), 3545-3547.
  4. [BD] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973.
  5. [DLM] J. Daughtry, A. Lambert, and B. Weinstock, Invariance of spectrum for representations of C*-algebras on Banach spaces, Proc. Amer. Math. Soc. 125 (1997), 189-198.
  6. [DS] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience Publ., New York, 1964.
  7. [G] D. Goldstein, Inverse closedness of C*-algebras in Banach algebras, Integral Equations Operator Theory 33 (1999), 172-174.
  8. [L] P. D. Lax, Symmetrizable linear transformations, Comm. Pure Appl. Math. 7 (1954), 633-647.
  9. [P1] T. Palmer, Classes of nonabelian, noncompact locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741.
  10. [P2] T. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. 1, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, 1994.
  11. [PT] V. Pták, Banach algebras with involutions, Manuscripta Math. 6 (1972), 245-290.
  12. [R] C. Rickart, Banach Algebras, Van Nostrand, 1960.
Studia Mathematica
2000/141/3
Export to PBN, Opens in new tab
Pages:
251-261
Main language of publication
English
Published
2000
Exact and natural sciences