# Centralizers for subsets of normed algebras

Studia Mathematica (2000)

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

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topYood, 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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- [5] I. Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153-183. Zbl0034.16604
- [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] C. J. Murphy, C*-algebras and Operator Theory, Academic Press, Boston, 1990.
- [8] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, 1960.

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