We prove a general ampliation homogeneity result for the quasicentral modulus of an n-tuple operators with respect to (p,1) Lorentz normed ideal. use this formula involving Hausdorff measure n-tuples commuting Hermitian spectrum which is contained in certain Cantor-like self-similar fractals.

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...

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 .

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...

Generalising the definition to commuting $d$-tuples of operators, a number authors have considered structural properties $m$-isometric, $n$-symmetric and $(m,n)$-isosymmetric in recent past. This note is an attempt take mystique out this extension show how large these follow from more familiar arguments used prove single operator version properties.

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 ...

It is well-known that an n-tuple $$(n\ge 3)$$ of commuting contractions does not posses isometric dilation, in general. Considering a class satisfying certain positivity assumption, we construct their dilations and consequently establish von Neumann inequality. The assumption related to Brehmer motivated by the study operator tuples Barik et al. (Trans Amer Math Soc 372(2):1429–1450, 2019).