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arXiv · 1810.05605

The reflexivity of hyperexpansions and their Cauchy dual operators

Shubhankar Podder·Deepak Kumar Pradhan
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Abstract

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 $TT^* + (T^*T)^{-1} \leqslant 2 I_{\mathcal H}.$

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Shubhankar Podder, Deepak Kumar Pradhan. 2018-10-12. The reflexivity of hyperexpansions and their Cauchy dual operators. https://arxiv.org/abs/1810.05605

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