On quasinilpotent equivalence of finite rank elements in Banach algebras

Heinrich Raubenheimer

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 589-596
  • ISSN: 0011-4642

Abstract

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We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.

How to cite

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Raubenheimer, Heinrich. "On quasinilpotent equivalence of finite rank elements in Banach algebras." Czechoslovak Mathematical Journal 60.3 (2010): 589-596. <http://eudml.org/doc/38029>.

@article{Raubenheimer2010,
abstract = {We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.},
author = {Raubenheimer, Heinrich},
journal = {Czechoslovak Mathematical Journal},
keywords = {maximal finite rank elements; quasinilpotent equivalence; maximal finite rank element; quasinilpotent equivalence},
language = {eng},
number = {3},
pages = {589-596},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On quasinilpotent equivalence of finite rank elements in Banach algebras},
url = {http://eudml.org/doc/38029},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Raubenheimer, Heinrich
TI - On quasinilpotent equivalence of finite rank elements in Banach algebras
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 589
EP - 596
AB - We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.
LA - eng
KW - maximal finite rank elements; quasinilpotent equivalence; maximal finite rank element; quasinilpotent equivalence
UR - http://eudml.org/doc/38029
ER -

References

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  1. Aupetit, B., Mouton, H. du T., Trace and determinant in Banach algebras, Stud. Math. 121 (1996), 115-136. (1996) Zbl0872.46028MR1418394
  2. Bonsall, F. F., Duncan, J., Complete Normed Algebras, Springer New York (1973). (1973) Zbl0271.46039MR0423029
  3. Colojoară, I., Foiaş, C., Quasi-nilpotent equivalence of not necessarily commuting operators, J. Math. Mech. 15 (1966), 521-540. (1966) MR0192344
  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). (1968) MR0394282
  5. Dalla, L., Giotopoulos, S., Katseli, N., 10.4064/sm-92-2-201-204, Stud. Math. 92 (1989), 201-204. (1989) Zbl0691.46036MR0986948DOI10.4064/sm-92-2-201-204
  6. Foiaş, C., Vasilescu, F.-H., 10.1016/0022-247X(70)90001-6, J. Math. Anal. Appl. 31 (1970), 473-486. (1970) MR0290146DOI10.1016/0022-247X(70)90001-6
  7. Giotopoulos, S., Roumeliotis, M., 10.1017/S0017089500008429, Glasgow Math. J. 33 (1991), 359-363. (1991) MR1127528DOI10.1017/S0017089500008429
  8. Harte, R., 10.4064/sm-117-1-73-77, Stud. Math. 117 (1995), 73-77. (1995) Zbl0837.46036MR1367694DOI10.4064/sm-117-1-73-77
  9. Mouton, S., Raubenheimer, H., 10.1023/A:1009717500980, Positivity 1 (1997), 305-317. (1997) Zbl0904.46036MR1660397DOI10.1023/A:1009717500980
  10. Müller, V., Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Birkhäuser Basel-Boston-Berlin (2003). (2003) MR1975356
  11. Puhl, J., The trace of finite and nuclear elements in Banach algebras, Czech. Math. J. 28 (1978), 656-676. (1978) Zbl0394.46041MR0506439
  12. Razpet, M., 10.1016/0022-247X(92)90304-V, J. Math. Anal. Appl. 166 (1992), 378-385. (1992) Zbl0802.46064MR1160933DOI10.1016/0022-247X(92)90304-V

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