On rank one elements

Robin Harte

Studia Mathematica (1995)

  • Volume: 117, Issue: 1, page 73-77
  • ISSN: 0039-3223

Abstract

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Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.

How to cite

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Harte, Robin. "On rank one elements." Studia Mathematica 117.1 (1995): 73-77. <http://eudml.org/doc/216242>.

@article{Harte1995,
author = {Harte, Robin},
journal = {Studia Mathematica},
keywords = {radical; rank one elements; scarcity lemma; semisimple Banach algebras},
language = {eng},
number = {1},
pages = {73-77},
title = {On rank one elements},
url = {http://eudml.org/doc/216242},
volume = {117},
year = {1995},
}

TY - JOUR
AU - Harte, Robin
TI - On rank one elements
JO - Studia Mathematica
PY - 1995
VL - 117
IS - 1
SP - 73
EP - 77
LA - eng
KW - radical; rank one elements; scarcity lemma; semisimple Banach algebras
UR - http://eudml.org/doc/216242
ER -

References

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  1. [1] B. Aupetit, A Primer on Spectral Theory, Springer, 1991. 
  2. [2] B. Aupetit and H. du T. Mouton, Spectrum preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100. Zbl0829.46039
  3. [3] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
  4. [4] J. B. Conway, Functions of One Complex Variable, Springer, 1978. 
  5. [5] R. E. Harte, Invertibility and Singularity, Dekker, 1988. 
  6. [6] R. A. Hirschfeld and B. E. Johnson, Spectral characterization of finite-dimensional algebras, Indag. Math. 34 (1972), 19-23. Zbl0232.46043
  7. [7] A. A. Jafarian and A. R. Sourour, Spectrum-preserving linear maps, J. Funct. Anal. 66 (1986), 255-261. Zbl0589.47003
  8. [8] H. du T. Mouton, On inessential ideals in Banach algebras, Quaestiones Math. 17 (1994), 59-66. Zbl0818.46053
  9. [9] H. du T. Mouton and H. Raubenheimer, On rank one and finite elements in Banach algebras, Studia Math. 104 (1993), 211-219. Zbl0814.46035
  10. [10] J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (1978), 656-676. Zbl0394.46041

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