International Journal of Functional Analysis, Operator Theory and Applications
Volume 10, Issue 2, Pages 73 - 80
(June 2018)
http://dx.doi.org/10.17654/FA010020073 |
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EXISTENCE OF INVARIANT SUBSPACES
R. Prakash
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Abstract:
Let A be a semisimple, regular, commutative and Tauberian Banach algebra with Gelfand space  Suppose that A has only trivial closed primary ideals at each  Let π be a nondegenerate representation of A on a Banach space X. We prove that, if π is not a character, then nontrivial invariant subspaces exist. |
| Keywords and phrases: commutative Banach algebra, primary ideal, representation, spectral subspace. |
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