Research Article

Asymptotic properties for compressions of two-isometries

Published in: Quaestiones Mathematicae
Volume 46 , issue 10 , 2023 , pages: 2177–2202

DOI: 10.2989/16073606.2022.2131651

Author(s): Laurian Suciu “Lucian Blaga” University of Sibiu, Romania

Keywords: 47A05 , 47A15 , 47A20 , 47A63 , Expansive operator , A-contraction , asymptotic limit

Abstract

The bounded linear operators T on a Hilbert space which have 2-isometric liftings S on are investigated in this paper. We refer to the structure of those operators in the case of general liftings, as well as for a more special type of such liftings S, namely for which is invariant to the orthogonal projection onto the kernel of S∗S − I. In this special case we describe the canonical triangulation of T induced by S, with entries expressed by operators close to contractions or isometries. Also, in this case we refer to some asymptotic properties of T and of its adjoint T∗ obtained by means of asymptotic limits associated to T∗ and T, relative to a lifting S for T. The canonical triangulations of T in this setting are described in detail, and as an application, the Wold type decomposition of a concave operator is obtained.

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