On a Spectral Version of Cartan�s Theorem

Bera, S and Chandel, VS and Londhe, M (2022) On a Spectral Version of Cartan�s Theorem. In: Journal of Geometric Analysis, 32 (2).

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Abstract

For a domain Ω in the complex plane, we consider the domain Sn(Ω) consisting of those n� n complex matrices whose spectrum is contained in Ω. Given a holomorphic self-map Ψ of Sn(Ω) such that Ψ (A) = A and the derivative of Ψ at A is identity for some A� Sn(Ω) , we investigate when the map Ψ would be spectrum-preserving. We prove that if the matrix A is either diagonalizable or non-derogatory then for most domains Ω , Ψ is spectrum-preserving on Sn(Ω). Further, when A is arbitrary, we prove that Ψ is spectrum-preserving on a certain analytic subset of Sn(Ω). © 2021, Mathematica Josephina, Inc.

Item Type:	Journal Article
Publication:	Journal of Geometric Analysis
Publisher:	Springer
Additional Information:	The copyright for this article belongs to Authors
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	27 Jan 2022 11:44
Last Modified:	27 Jan 2022 11:44
URI:	http://eprints.iisc.ac.in/id/eprint/71018

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