According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e. a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C *-algebraic analogue of this theor...

Kadison and Kastler introduced a metric on the set of all C∗-algebras on a fixed Hilbert space. In this paper structural properties of C∗-algebras which are close in this metric are examined. Our main result is that the property of having a positive answer to Kadison’s similarity problem transfers to close C∗-algebras. In establishing this result we answer questions about closeness of commutant...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

We give several characterizations of EP elements in C∗-algebras. The motivation for the factorization results comes in part from a recent paper by Drivaliaris, Karanasios and Pappas on Hilbert space operators. MSC: 46L05, 47A05

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We...

Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C∗algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C∗-algebras determined by an increasing sequence of positive integers, each divid...

In this paper we start with the development of a theory of presheaves on a lattice, in particular on the quantum lattice L(H) of closed subspaces of a complex Hilbert space H, and their associated etale spaces. Even in this early state the theory has interesting applications to the theory of operator algebras and the foundations of quantum mechanics. Among other things we can show that classica...

in this paper, we show that in each nite dimensional hilbert space, a frame of subspaces is an ultra bessel sequence of subspaces. we also show that every frame of subspaces in a nite dimensional hilbert space has frameness bound.

Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true”. The concept of Hilbert algebras was introduced in the 50-ties by L. Henkin and T. Skolem (under the name implicative models) for inve...