In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

We present a theorem which generalizes some known theorems on the existence of nonmeasurable (in various senses) sets of the form X+Y . Some additional related questions concerning measure, category and the algebra of Borel sets are also studied. Sierpiński showed in [14] that there exist two sets X, Y ⊆ R of Lebesgue measure zero such that their algebraic sum, i.e. the set X + Y = {x + y : x ∈...

We prove that the measure algebra M(G) of a locally compact group G is Connesamenable if and only if G is amenable.

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

For any complex valued functions over topological space F there exists a relation in von Neumann algebras of *-graded that is bounded on compact Hausdorff where for category- I, II, III commutative form 〖AW〗^* such to satisfy monotone complete C^* algebra suffice an isomorphic factor f the same tamed as W^* having generators η generic group η(G) 2-groups G_+ and G_- former being additive intege...

LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(...

LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(...

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that Inn(A) Inn0(A) is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, Inn(A) Inn0(A) is totally disconnected. Another consequence of our results is the following: Suppose A is the tran...

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on frequency space taking values in the expected algebra. The notion of linear quantum filters is introduced as some simple examples mentioned. 1 Spectral Analysis of ...