Trace and determinant in Banach algebras

• Autorzy: Bernard Aupetit , H. du T. Mouton
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H05: General theory of topological algebras
• 47A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 2
• Strony: 115-136

Daty

wydano

1996

otrzymano

1995-03-03

poprawiono

1996-06-28

Twórcy

autor

Bernard Aupetit

• Département de Mathématiques et de Statistique, Université Laval, Québec, Qué., Canada, G1K 7P4

autor

H. du T. Mouton

• Department of Electronic and Electrical Engineering, University of Stellenbosch, Stellenbosch, 7600 South Africa

Bibliografia

• [1] J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1-18.
• [2] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Berlin, 1979.
• [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.
• [5] B. Aupetit, A geometric characterization of algebraic varieties of $ℂ^2$, Proc. Amer. Math. Soc. 123 (1995), 3323-3327.
• [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.
• [8] B. Aupetit, A. Maouche and H. du T. Mouton, Trace and determinant in Jordan-Banach algebras, preprint.
• [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.
• [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.
• [12] R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23.
• [13] H. Kraljević and K. Veselić, On algebraic and spectrally finite Banach algebras, Glasnik Mat. 11 (1976), 291-318.
• [14] (H. du) T. Mouton and R. Raubenheimer, On rank one and finite elements of Banach algebras, Studia Math. 104 (1993), 211-219.
• [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.
• [17] W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974.
• [18] Y. Sun, A remark on the trace of some Riesz operators, Arch. Math. (Basel) 63 (1994), 530-534.
• [19] M. Trémon, Polynômes de degré minimum connectant deux projections dans une algèbre de Banach, Linear Algebra Appl. 64 (1985), 115-132.
• [20] H. K. Wimmer, Spectral radius and radius of convergence, Amer. Math. Monthly 81 (1974), 625-627.
• [21] J. Zemánek, Idempotents in Banach algebras, Bull. London Math. Soc. 11 (1979), 177-183.