Symmetric Banach *-algebras: invariance of spectrum

Bruce Barnes

Studia Mathematica (2000)

  • Volume: 141, Issue: 3, page 251-261
  • ISSN: 0039-3223

Abstract

top
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.

How to cite

top

Barnes, Bruce. "Symmetric Banach *-algebras: invariance of spectrum." Studia Mathematica 141.3 (2000): 251-261. <http://eudml.org/doc/216783>.

@article{Barnes2000,
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.},
author = {Barnes, Bruce},
journal = {Studia Mathematica},
keywords = {*-inverse closed; inverse closed; symmetric Banach *-algebra; spectral radius; involution; -norm},
language = {eng},
number = {3},
pages = {251-261},
title = {Symmetric Banach *-algebras: invariance of spectrum},
url = {http://eudml.org/doc/216783},
volume = {141},
year = {2000},
}

TY - JOUR
AU - Barnes, Bruce
TI - Symmetric Banach *-algebras: invariance of spectrum
JO - Studia Mathematica
PY - 2000
VL - 141
IS - 3
SP - 251
EP - 261
AB - 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.
LA - eng
KW - *-inverse closed; inverse closed; symmetric Banach *-algebra; spectral radius; involution; -norm
UR - http://eudml.org/doc/216783
ER -

References

top
  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. Zbl0646.47033
  3. [B3] B. Barnes, A note on invariance of spectrum for symmetric Banach *-algebras, Proc. Amer. Math. Soc. 126 (1998), 3545-3547. Zbl0905.46034
  4. [BD] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. Zbl0271.46039
  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. Zbl0860.46038
  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. Zbl0917.46055
  8. [L] P. D. Lax, Symmetrizable linear transformations, Comm. Pure Appl. Math. 7 (1954), 633-647. Zbl0057.34402
  9. [P1] T. Palmer, Classes of nonabelian, noncompact locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741. Zbl0396.22001
  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. Zbl0229.46054
  12. [R] C. Rickart, Banach Algebras, Van Nostrand, 1960. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.