On the Cauchy dual of closed range operators

Ezzahraoui, H.; Мbekhta, Mostafa; Zerouali, E. H.

doi:10.14232/actasm-018-020-2

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2021

2024

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Cited by 6 publications

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“…We conclude this note with some possible directions for further investigations. We would like to draw the reader's attention to the recent work [20], where the notion of the Cauchy dual operator has been generalized to the closed range operators. It would be interesting to know counterparts of the results in this paper for closed range operators.…”

Section: Discussionmentioning

confidence: 99%

The reflexivity of hyperexpansions and their Cauchy dual operators

Podder¹,

Pradhan²

2018

Preprint

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We discuss the reflexivity of hyperexpansions and their Cauchy dual operators. In particular, we show that any cyclic completely hyperexpansive operator is reflexive. We also establish the reflexivity of the Cauchy dual of an arbitrary 2-hyperexpansive operator. As a consequence, we deduce the reflexivity of the so-called Bergman-type operator, that is, a left-invertible operator T satisfying the inequality T T * + (T * T ) −1 2IH.

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Section: Discussionmentioning

confidence: 99%