Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid...

We study the vector-valued spectrum $\mathcal {M}_{u,\infty }(B_{\ell _2},B_{\ell _2})$, which is set of non-zero algebra homomorphisms from {A}_u(B_{\ell _2})$ (the uniformly continuous holomorphic functions on $B_{\ell _2}$) to

A known general program, designed to endow the quotient space U / B of unitary groups , C ∗ algebras ⊂ with an invariant Finsler metric, is applied obtain a metric for I ( H ) partial isometries Hilbert . group × where algebra bounded linear operators in Under this solution best approximation problem leads computation minimal geodesics space. We find solutions problem, and study properties obta...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as much as possible. Underlying theory, related to rigged Hilbert spaces and Lie algebras, is discussed elsewhere. OCIS codes 100.2000, 100.2980, 110.1085, 110.1758

If N ⊆M is an inclusion of type II1 factors of finite index on a separable Hilbert space, and if N has a Cartan subalgebra then we show that H(N ,M) = 0 for n ≥ 1. We also show that H cb(N ,M) = 0, n ≥ 1, for an arbitrary finite index inclusion N ⊆M of von Neumann algebras.