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arXiv · 1906.05215

m-isometric operators and their local properties

Z. J. Jablonski·I. B. Jung·J. Stochel
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Abstract

In this paper we give necessary and sufficient conditions for a bounded linear Hilbert space operator to be an $m$-isometry for an unspecified $m$ written in terms of conditions that are applied to "one vector at a time". We provide criteria for orthogonality of generalized eigenvectors of an (a priori unbounded) linear operator $T$ on an inner product space that correspond to distinct eigenvalues of modulus 1. We also discuss a similar question of when Jordan blocks of $T$ corresponding to distinct eigenvalues of modulus 1 are "orthogonal".

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Z. J. Jablonski, I. B. Jung, J. Stochel. 2019-06-12. m-isometric operators and their local properties. https://arxiv.org/abs/1906.05215

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