ABSTRACT
We investigate the operators T on a Hilbert space which have 2-isometric liftings S with the property . We show that such liftings are closely related to some extensions of T, which have upper triangular block matrices having contractive entries. We describe these extensions by the corresponding 2-isometric liftings, and respectively as regular A-contractions for some positive operators A. Also, we show that some extensions have Brownian isometric (or unitary) liftings and, in particular, we refer to expansive operators with such liftings.
Acknowledgments
The author was supported by a project financed by Lucian Blaga University of Sibiu and Hasso Plattner Foundation research Grants LBUS-IRG-2019-05. I would like to thank the referees for a careful reading of the manuscript and for useful suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).