Strongly irreducible factorization of quaternionic operators and Riesz decomposition theorem

Article Type

Research Article

Publication Title

Banach Journal of Mathematical Analysis


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.



Publication Date



Open Access, Green

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