EXISTENCE OF INVARIANT SUBSPACES
Copyright policy )EXISTENCE OF INVARIANT SUBSPACES
Summary: Let \(A\) be a semisimple, regular, commutative and Tauberian Banach algebra with Gelfand space \(\Delta(A)\). Suppose that \(A\) has only trivial closed primary ideals at each \(\gamma\in\Delta(A)\). Let \(\pi\) be a nondegenerate representation of \(A\) on a Banach space \(X\). We prove that, if \(\pi\) is not a character, then nontrivial invariant subspaces exist.
Representations of commutative topological algebras, representation, primary ideal, commutative Banach algebra, Abstract harmonic analysis, spectral subspace, invariant subspaces, Ideals, maximal ideals, boundaries
Representations of commutative topological algebras, representation, primary ideal, commutative Banach algebra, Abstract harmonic analysis, spectral subspace, invariant subspaces, Ideals, maximal ideals, boundaries
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