Symmetric Banach *-algebras: invariance of spectrum
Barnes, Bruce
Studia Mathematica, Tome 141 (2000), p. 251-261 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216783 
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     author = {Bruce Barnes},
     title = {Symmetric Banach *-algebras: invariance of spectrum},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {251-261},
     zbl = {0996.46021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv141i3p251bwm}
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Barnes, Bruce. Symmetric Banach *-algebras: invariance of spectrum. Studia Mathematica, Tome 141 (2000) pp. 251-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv141i3p251bwm/

[000] [B1] B. Barnes, The properties *-regularity and uniqueness of C*-norm in a general *-algebra, Trans. Amer. Math. Soc. 279 (1983), 841-859.

[001] [B2] B. Barnes, The spectrum of integral operators on Lebesgue space, J. Operator Theory 18 (1987), 115-132. | Zbl 0646.47033

[002] [B3] B. Barnes, A note on invariance of spectrum for symmetric Banach *-algebras, Proc. Amer. Math. Soc. 126 (1998), 3545-3547. | Zbl 0905.46034

[003] [BD] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. | Zbl 0271.46039

[004] [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. | Zbl 0860.46038

[005] [DS] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience Publ., New York, 1964.

[006] [G] D. Goldstein, Inverse closedness of C*-algebras in Banach algebras, Integral Equations Operator Theory 33 (1999), 172-174. | Zbl 0917.46055

[007] [L] P. D. Lax, Symmetrizable linear transformations, Comm. Pure Appl. Math. 7 (1954), 633-647. | Zbl 0057.34402

[008] [P1] T. Palmer, Classes of nonabelian, noncompact locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741. | Zbl 0396.22001

[009] [P2] T. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. 1, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, 1994.

[010] [PT] V. Pták, Banach algebras with involutions, Manuscripta Math. 6 (1972), 245-290. | Zbl 0229.46054

[011] [R] C. Rickart, Banach Algebras, Van Nostrand, 1960.