Spectral Disjointness and Invariant Subspaces

Year 2019, Volume: 1 Issue: 2, 56 - 65, 30.10.2019

Robin Harte

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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