Keywords: maximal finite rank elements; quasinilpotent equivalence
@article{CMJ_2010_60_3_a0,
author = {Raubenheimer, Heinrich},
title = {On quasinilpotent equivalence of finite rank elements in {Banach} algebras},
journal = {Czechoslovak Mathematical Journal},
pages = {589--596},
year = {2010},
volume = {60},
number = {3},
mrnumber = {2672403},
zbl = {1224.46091},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a0/}
}
Raubenheimer, Heinrich. On quasinilpotent equivalence of finite rank elements in Banach algebras. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 589-596. http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a0/
[1] Aupetit, B., Mouton, H. du T.: Trace and determinant in Banach algebras. Stud. Math. 121 (1996), 115-136. | MR | Zbl
[2] Bonsall, F. F., Duncan, J.: Complete Normed Algebras. Springer New York (1973). | MR | Zbl
[3] Colojoară, I., Foiaş, C.: Quasi-nilpotent equivalence of not necessarily commuting operators. J. Math. Mech. 15 (1966), 521-540. | MR
[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
[5] Dalla, L., Giotopoulos, S., Katseli, N.: The socle and finite-dimensionality of a semiprime Banach algebra. Stud. Math. 92 (1989), 201-204. | DOI | MR | Zbl
[6] Foiaş, C., Vasilescu, F.-H.: On the spectral theory of commutators. J. Math. Anal. Appl. 31 (1970), 473-486. | DOI | MR
[7] Giotopoulos, S., Roumeliotis, M.: Algebraic ideals of semiprime Banach algebras. Glasgow Math. J. 33 (1991), 359-363. | DOI | MR
[8] Harte, R.: On rank one elements. Stud. Math. 117 (1995), 73-77. | DOI | MR | Zbl
[9] Mouton, S., Raubenheimer, H.: More spectral theory in ordered Banach algebras. Positivity 1 (1997), 305-317. | DOI | MR | Zbl
[10] Müller, V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras. Birkhäuser Basel-Boston-Berlin (2003). | MR
[11] Puhl, J.: The trace of finite and nuclear elements in Banach algebras. Czech. Math. J. 28 (1978), 656-676. | MR | Zbl
[12] Razpet, M.: The quasinilpotent equivalence in Banach algebras. J. Math. Anal. Appl. 166 (1992), 378-385. | DOI | MR | Zbl