2019/11/08 by Edward J. Timko, Timko, Edward J.
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1911.03530
openalex publication_date 2019/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that for a single bounded operator A0 on a Hilbert \mathfrakH, if \mathfrakM⊂ \mathfrakH is hyperinvariant for A0, then the spectrum of A0|_\mathfrakM is contained in the spectrum of A0. In this note, we modify an example of Taylor to prove the following. There exist a quadruple A=(A1,A2,A3,A4) of commuting bounded Hilbert space operators and a hyperinvariant subspace \mathfrakX1 for A such that the Taylor joint spectrum of A restricted to \mathfrakX1 is a not a subset of the Taylor joint spectrum of A.