Spectral Disjointness and Invariant Subspaces

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Maltepe Journal of Mathematics
Volume:1 Issue:2
Spectral Disjointness and Invariant Subspaces

Spectral Disjointness and Invariant Subspaces

Authors : Robin HARTE

Pages : 56-65

View : 20 | Download : 6

Publication Date : 2019-10-30

Article Type : Research Paper

Abstract :Spectral disjointness confers a certain mutual independence on pairs of Banach algebra elements. Necessary and sufficient for full spectral disjointness of diagonal elements is that the structural idempotent is a holomorphic function of a block diagonal matrix, while a partial left-right spectral disjointness is sufficient for membership of the double commutant. For bounded linear Banach space operators with an invariant subspace, spectral disjointness for the restriction and quotient operators implies both hyperinvariance and reducing.
Keywords : spectral disjointness, invariant subspaces

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