On rank one and finite elements of Banach algebras

T. Mouton; H. Raubenheimer

Studia Mathematica (1993)

  • Volume: 104, Issue: 3, page 211-219
  • ISSN: 0039-3223

Abstract

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We give a spectral characterisation of rank one elements and of the socle of a semisimple Banach algebra.

How to cite

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Mouton, T., and Raubenheimer, H.. "On rank one and finite elements of Banach algebras." Studia Mathematica 104.3 (1993): 211-219. <http://eudml.org/doc/215970>.

@article{Mouton1993,
abstract = {We give a spectral characterisation of rank one elements and of the socle of a semisimple Banach algebra.},
author = {Mouton, T., Raubenheimer, H.},
journal = {Studia Mathematica},
keywords = {spectral characterization of rank one elements; socle of a semisimple Banach algebra},
language = {eng},
number = {3},
pages = {211-219},
title = {On rank one and finite elements of Banach algebras},
url = {http://eudml.org/doc/215970},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Mouton, T.
AU - Raubenheimer, H.
TI - On rank one and finite elements of Banach algebras
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 3
SP - 211
EP - 219
AB - We give a spectral characterisation of rank one elements and of the socle of a semisimple Banach algebra.
LA - eng
KW - spectral characterization of rank one elements; socle of a semisimple Banach algebra
UR - http://eudml.org/doc/215970
ER -

References

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  1. [1] B. Aupetit, Propriétés Spectrales des Algèbres de Banach, Springer, Berlin 1979. Zbl0409.46054
  2. [2] B. A. Barnes, G. J. Murphy, M. R. F. Smyth and T. T. West, Riesz and Fredholm Theory in Banach Algebras, Pitman, Boston 1982. Zbl0534.46034
  3. [3] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973. Zbl0271.46039
  4. [4] R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23. Zbl0232.46043
  5. [5] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
  6. [6] J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (1978), 656-676. Zbl0394.46041
  7. [7] Z. Słodkowski, On the subharmonicity of the capacity of the spectrum, Proc. Amer. Math. Soc. 81 (1981), 243-249. Zbl0407.46046

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