Commuting Contractive Operators

On Isometric Dilations of Product Systems of C-correspondences and Applications to Families of Contractions Associated to Higher-rank Graphs

Let E be a product system of C-correspondences over Nr 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between regular and -regular dilations discussed. It is in particular shown that a minimal isometric dilation is -regular if and only if it is doubly commuting. The c...

The Sums and Products of Commuting AC-Operators

Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.  

Standard Operator Models in the Polydisc, II

We first show that every γ-contractive commuting multioperator is unitarily equivalent to the restriction of S⊕W to an invariant subspace, where S is a backwards multi-shift and W a γ-isometry. We then describe γ-isometries in terms of (γ, 1)-isometries, and establish that under an additional assumption on T , W above can be chosen to be a commuting multioperator of isometries. Our methods prov...

Common Fixed Points of Generalized Contractive Maps in Cone Metric Spaces

Joint Extensions in Families of Contractive Commuting Operator Tuples

In this paper we systematically study extension questions in families of commuting operator tuples that are associated with the unit ball in C.