Trace and determinant in Banach algebras
Studia Mathematica (1996)
- Volume: 121, Issue: 2, page 115-136
- ISSN: 0039-3223
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topAupetit, Bernard, and Mouton, H.. "Trace and determinant in Banach algebras." Studia Mathematica 121.2 (1996): 115-136. <http://eudml.org/doc/216346>.
@article{Aupetit1996,
abstract = {We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.},
author = {Aupetit, Bernard, Mouton, H.},
journal = {Studia Mathematica},
keywords = {trace; determinant; semisimple Banach algebra},
language = {eng},
number = {2},
pages = {115-136},
title = {Trace and determinant in Banach algebras},
url = {http://eudml.org/doc/216346},
volume = {121},
year = {1996},
}
TY - JOUR
AU - Aupetit, Bernard
AU - Mouton, H.
TI - Trace and determinant in Banach algebras
JO - Studia Mathematica
PY - 1996
VL - 121
IS - 2
SP - 115
EP - 136
AB - We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
LA - eng
KW - trace; determinant; semisimple Banach algebra
UR - http://eudml.org/doc/216346
ER -
References
top- [1] J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1-18. Zbl0184.16502
- [2] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Berlin, 1979. Zbl0409.46054
- [3] B. Aupetit, A Primer on Spectral Theory, Universitext, Springer, New York, 1991.
- [4] B. Aupetit, Spectral characterization of the socle in Jordan-Banach algebras, Math. Proc. Cambridge Philos. Soc. 117 (1995), 479-489. Zbl0837.46040
- [5] B. Aupetit, A geometric characterization of algebraic varieties of , Proc. Amer. Math. Soc. 123 (1995), 3323-3327. Zbl0853.32014
- [6] B. Aupetit, Trace and spectrum preserving linear mappings in Jordan-Banach algebras, Monatsh. Math., to appear.
- [7] B. Aupetit and H. du T. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100. Zbl0829.46039
- [8] B. Aupetit, A. Maouche and H. du T. Mouton, Trace and determinant in Jordan-Banach algebras, preprint. Zbl1013.46040
- [9] B. A. Barnes, G. J. Murphy, M. R. F. Smyth and T. T. West, Riesz and Fredholm Theory in Banach Algebras, Res. Notes in Math. 67, Pitman, Boston, 1982. Zbl0534.46034
- [10] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Ergeb. Math. Grenzgeb. 80, Springer, Berlin, 1973.
- [11] J. Dieudonné, History of Functional Analysis, Notas Mat. 49, North-Holland, Amsterdam, 1981. Zbl0478.46001
- [12] R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23. Zbl0232.46043
- [13] H. Kraljević and K. Veselić, On algebraic and spectrally finite Banach algebras, Glasnik Mat. 11 (1976), 291-318. Zbl0354.46031
- [14] (H. du) T. Mouton and R. Raubenheimer, On rank one and finite elements of Banach algebras, Studia Math. 104 (1993), 211-219. Zbl0814.46035
- [15] A. Pietsch, Eigenvalues and s-Numbers, Cambridge Stud. Adv. Math. 13, Cambridge University Press, Cambridge, 1987.
- [16] J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (103) (1978), 656-676. Zbl0394.46041
- [17] W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974. Zbl0278.26001
- [18] Y. Sun, A remark on the trace of some Riesz operators, Arch. Math. (Basel) 63 (1994), 530-534. Zbl0817.47023
- [19] M. Trémon, Polynômes de degré minimum connectant deux projections dans une algèbre de Banach, Linear Algebra Appl. 64 (1985), 115-132. Zbl0617.46054
- [20] H. K. Wimmer, Spectral radius and radius of convergence, Amer. Math. Monthly 81 (1974), 625-627. Zbl0291.15021
- [21] J. Zemánek, Idempotents in Banach algebras, Bull. London Math. Soc. 11 (1979), 177-183. Zbl0429.46029
Citations in EuDML Documents
top- Matej Brešar, Peter Šemrl, Finite rank elements in semisimple Banach algebras
- Heinrich Raubenheimer, On quasinilpotent equivalence of finite rank elements in Banach algebras
- Rudi M. Brits, Heinrich Raubenheimer, Finite spectra and quasinilpotent equivalence in Banach algebras
- Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz, The index for Fredholm elements in a Banach algebra via a trace II
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