Unitary N-dilations for Tuples of Commuting Matrices

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

Standard dilations of q-commuting tuples

Here we study dilations of q-commuting tuples. In [BBD] the authors gave the correspondence between the two standard dilations of commuting tuples and here these results have been extended to q-commuting tuples. We are able to do this when q-coefficients ‘qij ’ are of modulus one. We introduce ‘maximal q-commuting subspace ’ of a n-tuple of operators and ‘standard q-commuting dilation’. Our mai...

Standard Models under Polynomial Positivity Conditions

We develop standard models for commuting tuples of bounded linear operators on a Hilbert space under certain polynomial positivity conditions, generalizing the work of V. Müller and F.-H. Vasilescu in [6], [14]. As a consequence of the model, we prove a von Neumann-type inequality for such tuples. Up to similarity, we obtain the existence of in a certain sense “unitary” dilations.

Commutant lifting theorem for n-tuples of contractions

We show that the commutant lifting theorem for n-tuples of commuting contractions with regular dilations fails to be true. A positive answer is given for operators which ”double intertwine” given n-tuples of contractions. The commutant lifting theorem is one of the most important results of the Sz. Nagy—Foias dilation theory. It is usually stated in the following way: Theorem. Let T and T ′ be ...

Contractive Hilbert Modules and Their Dilations over Natural Function Algebras

In this note, we show that quasi-free Hilbert modules R defined over natural function algebras satisfying a certain positivity condition, defined via the hereditary functional calculus, admit a dilation (actually a co-extension) to the Hardy module over the polydisk. An explicit realization of the dilation space is given along with the isometric embedding of the module R in it. Some consequence...