# Symmetric Banach *-algebras: invariance of spectrum

Studia Mathematica (2000)

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

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topBarnes, 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- [B1] B. Barnes, The properties *-regularity and uniqueness of C*-norm in a general *-algebra, Trans. Amer. Math. Soc. 279 (1983), 841-859.
- [B2] B. Barnes, The spectrum of integral operators on Lebesgue space, J. Operator Theory 18 (1987), 115-132. Zbl0646.47033
- [B3] B. Barnes, A note on invariance of spectrum for symmetric Banach *-algebras, Proc. Amer. Math. Soc. 126 (1998), 3545-3547. Zbl0905.46034
- [BD] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. Zbl0271.46039
- [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
- [DS] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience Publ., New York, 1964.
- [G] D. Goldstein, Inverse closedness of C*-algebras in Banach algebras, Integral Equations Operator Theory 33 (1999), 172-174. Zbl0917.46055
- [L] P. D. Lax, Symmetrizable linear transformations, Comm. Pure Appl. Math. 7 (1954), 633-647. Zbl0057.34402
- [P1] T. Palmer, Classes of nonabelian, noncompact locally compact groups, Rocky Mountain J. Math. 8 (1978), 683-741. Zbl0396.22001
- [P2] T. Palmer, Banach Algebras and the General Theory of *-Algebras, Vol. 1, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, 1994.
- [PT] V. Pták, Banach algebras with involutions, Manuscripta Math. 6 (1972), 245-290. Zbl0229.46054
- [R] C. Rickart, Banach Algebras, Van Nostrand, 1960.

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