"Strongly irreducible factorization of quaternionic operators and Riesz" by Santhosh Kumar Pamula
 

Strongly irreducible factorization of quaternionic operators and Riesz decomposition theorem

Article Type

Research Article

Publication Title

Banach Journal of Mathematical Analysis

Abstract

Let H be a right quaternionic Hilbert space and let T be a bounded quaternionic normal operator on H. In this article, we show that T can be factorized in a strongly irreducible sense, that is, for any δ> 0 there exist a compact operator K with the norm ‖ K‖ < δ, a partial isometry W and a strongly irreducible operator S on H such that T=(W+K)S.We illustrate our result with an example. In addition, we discuss the quaternionic version of the Riesz decomposition theorem and obtain a consequence that if the S-spectrum of a bounded (need not be normal) quaternionic operator is disconnected by a pair of disjoint axially symmetric closed subsets, then the operator is strongly reducible.

DOI

10.1007/s43037-020-00084-9

Publication Date

1-1-2021

Comments

Open Access, Green

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