Trace and determinant in Banach algebras

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1. [1] J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1-18. Zbl0184.16502
2. [2] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Berlin, 1979. Zbl0409.46054
3. [3] B. Aupetit, A Primer on Spectral Theory, Universitext, Springer, New York, 1991. 
4. [4] B. Aupetit, Spectral characterization of the socle in Jordan-Banach algebras, Math. Proc. Cambridge Philos. Soc. 117 (1995), 479-489. Zbl0837.46040
5. [5] B. Aupetit, A geometric characterization of algebraic varieties of ${ℂ}^2$, Proc. Amer. Math. Soc. 123 (1995), 3323-3327. Zbl0853.32014
6. [6] B. Aupetit, Trace and spectrum preserving linear mappings in Jordan-Banach algebras, Monatsh. Math., to appear. 
7. [7] B. Aupetit and H. du T. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100. Zbl0829.46039
8. [8] B. Aupetit, A. Maouche and H. du T. Mouton, Trace and determinant in Jordan-Banach algebras, preprint. Zbl1013.46040
9. [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. [10] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Ergeb. Math. Grenzgeb. 80, Springer, Berlin, 1973. 
11. [11] J. Dieudonné, History of Functional Analysis, Notas Mat. 49, North-Holland, Amsterdam, 1981. Zbl0478.46001
12. [12] R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23. Zbl0232.46043
13. [13] H. Kraljević and K. Veselić, On algebraic and spectrally finite Banach algebras, Glasnik Mat. 11 (1976), 291-318. Zbl0354.46031
14. [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. [15] A. Pietsch, Eigenvalues and s-Numbers, Cambridge Stud. Adv. Math. 13, Cambridge University Press, Cambridge, 1987. 
16. [16] J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (103) (1978), 656-676. Zbl0394.46041
17. [17] W. Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974. Zbl0278.26001
18. [18] Y. Sun, A remark on the trace of some Riesz operators, Arch. Math. (Basel) 63 (1994), 530-534. Zbl0817.47023
19. [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. [20] H. K. Wimmer, Spectral radius and radius of convergence, Amer. Math. Monthly 81 (1974), 625-627. Zbl0291.15021
21. [21] J. Zemánek, Idempotents in Banach algebras, Bull. London Math. Soc. 11 (1979), 177-183. Zbl0429.46029

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