Centralizers for subsets of normed algebras

Bertram Yood

Studia Mathematica (2000)

  • Volume: 142, Issue: 1, page 1-6
  • ISSN: 0039-3223

Abstract

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Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either c x c - 1 = x for all c ∈ H or s u p ∥ c x c - 1 ∥ : c ∈ H = ∞ . In that case the set of x ∈ A for which the sup is finite is the centralizer of H.

How to cite

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Yood, Bertram. "Centralizers for subsets of normed algebras." Studia Mathematica 142.1 (2000): 1-6. <http://eudml.org/doc/216786>.

@article{Yood2000,
abstract = {Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either $cxc^\{-1\} = x$ for all c ∈ H or $sup \{∥cxc^\{-1\}∥ : c ∈ H\} = ∞ $. In that case the set of x ∈ A for which the sup is finite is the centralizer of H.},
author = {Yood, Bertram},
journal = {Studia Mathematica},
keywords = {normed algebras; Banach algebras; centralizers; socle},
language = {eng},
number = {1},
pages = {1-6},
title = {Centralizers for subsets of normed algebras},
url = {http://eudml.org/doc/216786},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Yood, Bertram
TI - Centralizers for subsets of normed algebras
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 1
SP - 1
EP - 6
AB - Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either $cxc^{-1} = x$ for all c ∈ H or $sup {∥cxc^{-1}∥ : c ∈ H} = ∞ $. In that case the set of x ∈ A for which the sup is finite is the centralizer of H.
LA - eng
KW - normed algebras; Banach algebras; centralizers; socle
UR - http://eudml.org/doc/216786
ER -

References

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  1. [1] B. Aupetit, Propriétés spectrales des algèbres de Banach, Springer, New York, 1979. Zbl0409.46054
  2. [2] J. A. Deddens, Another description of nest algebras, in: Hilbert Space Operators, Lecture Notes in Math. 693, Springer, New York, 1978, 77-86. 
  3. [3] D. A. Herrero, A note on similarities of operators, Rev. Un. Mat. Argentina 36 (1990), 138-145. Zbl0781.47027
  4. [4] N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Publ. 37, Amer. Math. Soc., Providence, 1956. 
  5. [5] I. Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153-183. Zbl0034.16604
  6. [6] C. Le Page, Sur quelques conditions entraînant la commutativité dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 265 (1967), 235-237. Zbl0158.14102
  7. [7] C. J. Murphy, C*-algebras and Operator Theory, Academic Press, Boston, 1990. 
  8. [8] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, 1960. 

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