# Finite rank elements in semisimple Banach algebras

Studia Mathematica (1998)

- Volume: 128, Issue: 3, page 287-298
- ISSN: 0039-3223

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topBrešar, Matej, and Šemrl, Peter. "Finite rank elements in semisimple Banach algebras." Studia Mathematica 128.3 (1998): 287-298. <http://eudml.org/doc/216487>.

@article{Brešar1998,

abstract = {Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.},

author = {Brešar, Matej, Šemrl, Peter},

journal = {Studia Mathematica},

keywords = {rank; semisimple Banach algebra; decomposability; indecomposable elements},

language = {eng},

number = {3},

pages = {287-298},

title = {Finite rank elements in semisimple Banach algebras},

url = {http://eudml.org/doc/216487},

volume = {128},

year = {1998},

}

TY - JOUR

AU - Brešar, Matej

AU - Šemrl, Peter

TI - Finite rank elements in semisimple Banach algebras

JO - Studia Mathematica

PY - 1998

VL - 128

IS - 3

SP - 287

EP - 298

AB - Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.

LA - eng

KW - rank; semisimple Banach algebra; decomposability; indecomposable elements

UR - http://eudml.org/doc/216487

ER -

## References

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- [4] M. Brešar and P. Šemrl, Derivations mapping into the socle, Math. Proc. Cambridge Philos. Soc. 120 (1996), 339-346.
- [5] J. M. G. Fell and R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 1, Academic Press, Boston, 1988. Zbl0652.46050
- [6] A. A. Jafarian and A. R. Sourour, Spectrum preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
- [7] B. V. Limaye, A spectral characterization of operators having rank k, Linear Algebra Appl. 143 (1991), 57-66. Zbl0721.47026
- [8] T. Mouton and H. Raubenheimer, On rank one and finite elements of Banach algebras, Studia Math. 104 (1993), 211-219. Zbl0814.46035
- [9] P. Nylen and L. Rodman, Approximation numbers and Yamamoto's theorem in Banach algebras, Integral Equations Operator Theory 13 (1990), 728-749. Zbl0731.46028
- [10] C. E. Rickart, General Theory of Banach Algebras, The University Series in Higher Mathematics, D. van Nostrand, 1960. Zbl0095.09702

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