we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Several versions of approximate conjugacy for minimal dynamical systems are introduced. Relation between approximate conjugacy and corresponding crossed product C∗-algebras is discussed. For the Cantor minimal systems, a complete description is given for these relations via K-theory and C∗-algebras. For example, it is shown that two Cantor minimal systems are approximately τ -conjugate if and o...

We establish basic results of complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds (such as algebras of Bohr’s holomorphic almost periodic functions on tube domains or algebras of all fibrewise bounded holomorphic functions arising, e.g., in the corona problem for H∞). In particular, in this context we obtain results on holomorphic extension f...

We investigate the triangulated hull of orbit categories perfect derived category and bounded a ring concerning power suspension functor. It turns out that will correspond to full subcategory compact objects certain periodic complexes. This specializes Stai Zhao's result when is finite dimensional algebra with global dimension over field. As first application, if $A,B$ are flat algebras commuta...

We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite tree structure associated with the underlying Hilbert space. These shifts arise naturally through weighted versions of certain representations of the Cuntz C...

In this paper we study weakly almost periodic and uniformly continuous functionals on the Orlicz Figà-Talamanca Herz algebras associated to a locally compact group. We show that unique invariant mean exists space of functionals. also characterise discrete groups in terms inclusion inside

In [V. Mathai, K-theory of twisted group C∗-algebras and positive scalar curvature, Contemp. Math. 231 (1999) 203–225], we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz., the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundame...

We use non-standard analysis to define a category ?Hilb suitable for categorical quantum mechanics in arbitrary separable Hilbert spaces, and we show that standard bounded operators can be suitably embedded in it. We show the existence of unital special commutative †-Frobenius algebras, and we conclude ?Hilb to be compact closed, with partial traces and a Hilbert-Schmidt inner product on morphi...