Joint spectrum of matrix and operator tuples on spaces over bi complex numbers

2024/08/26 by Akshay S. Rane, Rane, Akshay
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2409.09038

openalex publication_date 2024/08/26 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/28

Abstract

In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum of a bounded operator on a bi complex Hilbert space is bounded. But this is not the case here. Even the set of joint eigenvalues of matrix tuples is unbounded.

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