We study actions of “compact quantum groups” on “finite quantum spaces”. According to Woronowicz and to general C-algebra philosophy these correspond to certain coactions v : A → A ⊗ H . Here A is a finite dimensional C-algebra, and H is a certain special type of Hopf ∗-algebra. If v preserves a positive linear form φ : A → C, a version of Jones’ “basic construction” applies. This produces a ce...

We study residually finite-dimensional (or RFD) operator algebras which may not be self-adjoint. An algebra RFD while simultaneously possessing completely isometric representations whose generating C⁎-algebra is RFD. This has provided many hurdles in characterizing residual finite-dimensionality for algebras. To better understand the elusive behavior, we explore C⁎-covers of an algebra. First, ...

We develop a complete theory of non-formal deformation quantization on the cotangent bundle weakly exponential Lie group. An appropriate integral formula for star-product is introduced together with suitable space functions which well defined. This becomes Fréchet algebra as pre-C*-algebra. Basic properties are proved, and extension to Hilbert an distributions given. A C*-algebra observables st...

In this paper, we extend the constructions of Boava and Exel to present C∗-algebra associated with an injective endomorphism a group finite cokernel as partial algebra consequently crossed product. With representation, another way study such C∗-algebras, only using tools from products.

The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-...

Abstract Let G be a finite group, let A an infinite-dimensional stably simple unital C*-algebra, and $\alpha \colon \to {\operatorname {Aut}} (A)$ action of on which has the weak tracial Rokhlin property. $A^{\alpha }$ fixed point algebra. Then radius comparison satisfies ${\operatorname {rc}} (A^{\alpha }) \leq ( C^* (G, A, \alpha ) ({1}/{{{\operatorname{card}}} (G))} \cdot . The inclusion in ...

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

It is well known that the adjacency algebra of an association scheme has the standard character. In this paper we first define the concept of standard character for C-algebras and we say that a C-algebra has the standard character condition if it has the standard character. Then we investigate some properties of C-algebras which have the standard character condition and prove that under some co...

Let X be a compact metric space, let A unital AH-algebra with large matrix sizes, and B stably finite C∗-algebra. Then we give lower bound for the radius of comparison C(X)⊗B prove that dimension-rank ratio satisfies drr(A)=drr(C(X)⊗A). We also class AH-algebras rc(C(X)⊗A)=rc(A). further exact Z-stable C∗-algebras nonzero comparison.

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C∗-correspondences and Cuntz– Pimsner algebras. We show that the C∗-algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura’s topological-graph bimodule, and that the C∗-algebra generated by...