On Taylor and other joint spectra for commuting n-tuples of operators

m-Isometric Commuting Tuples of Operators on a Hilbert Space

We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic properties of these tuples of commuting operators and we explore several examples. In particular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a the...

Unitary N-dilations for Tuples of Commuting Matrices

We show that whenever a contractive k-tuple T on a finite dimensional space H has a unitary dilation, then for any fixed degree N there is a unitary k-tuple U on a finite dimensional space so that q(T ) = PHq(U)|H for all polynomials q of degree at most N .

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.

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

Isometric Dilations of Non-commuting Finite Rank N-tuples

A contractive n-tuple A = (A1, . . . , An) has a minimal joint isometric dilation S = (S1, . . . , Sn) where the Si’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra S generated by S is completely described in terms of the properties of A. This provid...