Dilation theory is a paradigm for studying operators by way of exhibiting an operator as a
compression of another operator which is in some sense well behaved. For example, every …

We show that for every pair of matrices (S, P), having the closed symmetrized bidisc Γ as a
spectral set, there is a one dimensional complex algebraic variety Λ in Γ such that for every …

A commuting pair of operators (S, P) on a Hilbert space 𝓗 is said to be a Γ-contraction if the
symmetrized bidisc Γ=(z1+ z2, z1z2):| z1|,| z2|≤ 1 is a spectral set of the tuple (S, P). In this …

A set $ V $ in a domain $ U $ in $\mathbb {C}^ n $ has the norm-preserving extension
property if every bounded holomorphic function on $ V $ has a holomorphic extension to $ U …

We show that a weighted Bergman space on the polydisc splits up into the orthogonal direct
sum of subspaces, each corresponding to an irreducible representation of the symmetric …

A pair of commuting operators (S, P) defined on a Hilbert space 𝓗 for which the closed
symmetrized bidisc Γ=(z1+ z2, z1z2):| z1|≤ 1,| z2|≤ 1⊆ ℂ2 is a spectral set is called a Γ …

There are three new things in this paper about the open symmetrized bidisk G={(z 1+ z 2, z 1
z 2):| z 1|,| z 2|< 1}. They are, in the order in which they will be proved,(1) The Realization …

The tetrablock, roughly speaking, is the set of all linear fractional maps that map the open
unit disc to itself. A formal definition of this inhomogeneous domain is given below. This …

In this paper, we fully characterize maximal representations of a C*-correspondence,
thereby strengthening several earlier results. We demonstrate the maximality criteria through …

(4) There is a one-to-one correspondence between operator-valued contractive holomorphic
functions and canonical model triples. This pertains to the new realization formula …