ArticleOriginal scientific text

Title

On rank one elements

Authors 1

Affiliations

  1. 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

  1. B. Aupetit, A Primer on Spectral Theory, Springer, 1991.
  2. B. Aupetit and H. du T. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100.
  3. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
  4. J. B. Conway, Functions of One Complex Variable, Springer, 1978.
  5. R. E. Harte, Invertibility and Singularity, Dekker, 1988.
  6. R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23.
  7. A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261.
  8. H. du T. Mouton, On inessential ideals in Banach algebras, Quaestiones Math. 17 (1994), 59-66.
  9. H. du T. Mouton and H. Raubenheimer, On rank one and finite elements in Banach algebras, Studia Math. 104 (1993), 211-219.
  10. J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (1978), 656-676.
Pages:
73-77
Main language of publication
English
Received
1995-03-15
Accepted
1995-06-21
Published
1995
Exact and natural sciences