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Keywords:
maximal finite rank elements; quasinilpotent equivalence
Summary:
We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.
References:
[1] Aupetit, B., Mouton, H. du T.: Trace and determinant in Banach algebras. Stud. Math. 121 (1996), 115-136. MR 1418394 | Zbl 0872.46028
[2] Bonsall, F. F., Duncan, J.: Complete Normed Algebras. Springer New York (1973). MR 0423029 | Zbl 0271.46039
[3] Colojoară, I., Foiaş, C.: Quasi-nilpotent equivalence of not necessarily commuting operators. J. Math. Mech. 15 (1966), 521-540. MR 0192344
[4] Colojoară, I., Foiaş, C.: Theory of generalized spectral operators. Mathematics and its Applications, vol. 9. Gordon and Breach, Science Publishers New York-London-Paris (1968). MR 0394282
[5] Dalla, L., Giotopoulos, S., Katseli, N.: The socle and finite-dimensionality of a semiprime Banach algebra. Stud. Math. 92 (1989), 201-204. MR 0986948 | Zbl 0691.46036
[6] Foiaş, C., Vasilescu, F.-H.: On the spectral theory of commutators. J. Math. Anal. Appl. 31 (1970), 473-486. DOI 10.1016/0022-247X(70)90001-6 | MR 0290146
[7] Giotopoulos, S., Roumeliotis, M.: Algebraic ideals of semiprime Banach algebras. Glasgow Math. J. 33 (1991), 359-363. DOI 10.1017/S0017089500008429 | MR 1127528
[8] Harte, R.: On rank one elements. Stud. Math. 117 (1995), 73-77. MR 1367694 | Zbl 0837.46036
[9] Mouton, S., Raubenheimer, H.: More spectral theory in ordered Banach algebras. Positivity 1 (1997), 305-317. DOI 10.1023/A:1009717500980 | MR 1660397 | Zbl 0904.46036
[10] Müller, V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras. Birkhäuser Basel-Boston-Berlin (2003). MR 1975356
[11] Puhl, J.: The trace of finite and nuclear elements in Banach algebras. Czech. Math. J. 28 (1978), 656-676. MR 0506439 | Zbl 0394.46041
[12] Razpet, M.: The quasinilpotent equivalence in Banach algebras. J. Math. Anal. Appl. 166 (1992), 378-385. DOI 10.1016/0022-247X(92)90304-V | MR 1160933 | Zbl 0802.46064
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