Finite dimensional invariant subspaces for algebras of linear operators and amenable Banach algebras

We study a finite dimensional invariant subspace property similar to Fan's Theorem on semigroups for arbitrary Banach algebras A in terms of amenability of X(A,ϕ), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character ϕ. As a consequence, we of...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 510; pp. 329 - 345
Main Authors: Nasr-Isfahani, Rasoul, Nemati, Mehdi, Shahmoradi, Somayeh
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2016
Subjects:
Banach algebra
Character amenable
Finite dimensional invariant subspace
Fixed point property
Locally compact group
Maximal element
15A30
43A15
Banach algebra
43A20
Maximal element
43A10
Fixed point property
Locally compact group
43A07
46H05
Finite dimensional invariant subspace
Character amenable
ISSN:0024-3795, 1873-1856
Online Access:Get full text
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Summary:We study a finite dimensional invariant subspace property similar to Fan's Theorem on semigroups for arbitrary Banach algebras A in terms of amenability of X(A,ϕ), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character ϕ. As a consequence, we offer some applications to the measure algebra M(G) and the generalized Fourier algebra Ap(G) of a locally compact group G.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.08.028