Download PDF - On rank one elements
ArticleOriginal scientific text
Title
On rank one elements
Authors 1
Affiliations
- School of Mathematics, Trinity College, Dublin, Ireland
Abstract
Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.
Bibliography
- B. Aupetit, A Primer on Spectral Theory, Springer, 1991.
- B. Aupetit and H. du T. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100.
- F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
- J. B. Conway, Functions of One Complex Variable, Springer, 1978.
- R. E. Harte, Invertibility and Singularity, Dekker, 1988.
- R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23.
- A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261.
- H. du T. Mouton, On inessential ideals in Banach algebras, Quaestiones Math. 17 (1994), 59-66.
- H. du T. Mouton and H. Raubenheimer, On rank one and finite elements in Banach algebras, Studia Math. 104 (1993), 211-219.
- J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (1978), 656-676.