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

TL;DR
This paper extends the concept of joint spectrum and eigenvalues to matrix and operator tuples on bi-complex Hilbert spaces, revealing unboundedness properties unlike classical spectra.
Contribution
It introduces a generalized notion of joint spectrum for matrices and operators on bi-complex spaces, highlighting differences from traditional spectral properties.
Findings
Joint eigenvalues can be unbounded in bi-complex spaces.
The joint spectrum of operator tuples is not necessarily bounded.
Classical spectral boundedness does not hold in bi-complex settings.
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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Taxonomy
TopicsAdvanced Topics in Algebra · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods
