5 research outputs found
Pairs of inner projections and two applications
Orthogonal projections onto closed subspaces of of the
form for inner functions on
are referred to as inner projections, where
denotes the Hardy space over the open unit polydisc . In this
paper, we classify pairs of commuting inner projections. We also present two
seemingly independent applications: the first is an answer to a question posed
by R. G. Douglas, and the second is a complete classification of partially
isometric truncated Toeplitz operators with inner symbols on the polydisc.Comment: 18 page
\clw-hypercontractions and their model
We revisit the study of -hypercontractions corresponding to a single
weight sequence introduced by Olofsson in
\cite{O} and find an analogue of Nagy-Foias characteristic function in this
setting. Explicit construction of characteristic functions is obtained and it
is shown to be a complete unitary invariant. By considering a multi-weight
sequence \clw and \clw-hypercontractions we extend Olofsson's work \cite{O}
in the multi-variable setting. Model for \clw-hypercontractions is obtained
by finding their dilations on certain weighted Bergman spaces over the polydisc
corresponding to the multi-weight sequence \clw. This recovers and provides a
different proof of the earlier work of Curto and Vasilescu \cite{CVPoly, CV}
for -contractive multi-operators through a particular choice of
multi-weight sequence.Comment: 31 pages, updated version, comments are welcom