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.
@article{bwmeta1.element.bwnjournal-article-smv121i2p115bwm,
author = {Bernard Aupetit and H. Mouton},
title = {Trace and determinant in Banach algebras},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {115-136},
zbl = {0872.46028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv121i2p115bwm}
}
Aupetit, Bernard; Mouton, H. Trace and determinant in Banach algebras. Studia Mathematica, Tome 119 (1996) pp. 115-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv121i2p115bwm/
[00000] [1] J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1-18. | Zbl 0184.16502
[00001] [2] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Berlin, 1979. | Zbl 0409.46054
[00002] [3] B. Aupetit, A Primer on Spectral Theory, Universitext, Springer, New York, 1991.
[00003] [4] B. Aupetit, Spectral characterization of the socle in Jordan-Banach algebras, Math. Proc. Cambridge Philos. Soc. 117 (1995), 479-489. | Zbl 0837.46040
[00004] [5] B. Aupetit, A geometric characterization of algebraic varieties of , Proc. Amer. Math. Soc. 123 (1995), 3323-3327. | Zbl 0853.32014
[00005] [6] B. Aupetit, Trace and spectrum preserving linear mappings in Jordan-Banach algebras, Monatsh. Math., to appear.
[00006] [7] B. Aupetit and H. du T. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100. | Zbl 0829.46039
[00007] [8] B. Aupetit, A. Maouche and H. du T. Mouton, Trace and determinant in Jordan-Banach algebras, preprint. | Zbl 1013.46040
[00008] [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. | Zbl 0534.46034
[00009] [10] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Ergeb. Math. Grenzgeb. 80, Springer, Berlin, 1973.
[00010] [11] J. Dieudonné, History of Functional Analysis, Notas Mat. 49, North-Holland, Amsterdam, 1981. | Zbl 0478.46001
[00011] [12] R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23. | Zbl 0232.46043
[00012] [13] H. Kraljević and K. Veselić, On algebraic and spectrally finite Banach algebras, Glasnik Mat. 11 (1976), 291-318. | Zbl 0354.46031
[00013] [14] (H. du) T. Mouton and R. Raubenheimer, On rank one and finite elements of Banach algebras, Studia Math. 104 (1993), 211-219. | Zbl 0814.46035
[00014] [15] A. Pietsch, Eigenvalues and s-Numbers, Cambridge Stud. Adv. Math. 13, Cambridge University Press, Cambridge, 1987.
[00015] [16] J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (103) (1978), 656-676. | Zbl 0394.46041
[00016] [17] W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974. | Zbl 0278.26001
[00017] [18] Y. Sun, A remark on the trace of some Riesz operators, Arch. Math. (Basel) 63 (1994), 530-534. | Zbl 0817.47023
[00018] [19] M. Trémon, Polynômes de degré minimum connectant deux projections dans une algèbre de Banach, Linear Algebra Appl. 64 (1985), 115-132. | Zbl 0617.46054
[00019] [20] H. K. Wimmer, Spectral radius and radius of convergence, Amer. Math. Monthly 81 (1974), 625-627. | Zbl 0291.15021
[00020] [21] J. Zemánek, Idempotents in Banach algebras, Bull. London Math. Soc. 11 (1979), 177-183. | Zbl 0429.46029