Spectral inclusion for doubly commuting subnormal $n$-tuples

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 .

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...

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...

The Lifting Problem for Hyponormal Pairs of Commuting Subnormal Operators

We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of RC, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality. Our tools include the use of 2-variable weighted...