The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture and Atiyah’s L-index theorem implies that the range consists of the integers. If the group is not torsion free, Baum and Connes conjecture ...

LetA be a finite-dimensional commutative algebra over the complex numbers with nonzero multiplicative identity element e. Let M denote the set of homomorphisms from A onto the complex numbers. Thus we get a homomorphism from A into the algebra of complex-valued functions on M, with respect to pointwise addition and multiplication of functions, by sending an element x of A to the function on M w...

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

We compare the K-theory and K-homology of the well known CAR algebra. While the K0 group is infinitely generated, we show that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology group is very large. These results give some insight into the K-homology of AF-algebras. 1. The CAR algebra We...

In this paper, we apply the concept of fuzzy set to ideals and closed ideals in B-algebras. The notion of a fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of fuzzy B-algebra is investigated. Keywords—B-algebras, fuzzy sets, fuzzy ideals, homomorphism, fuzzy closed ideals, homomorphism, equivalence relation, level cut, product of ...

A noncommutative algebra A, called an algebraic noncommutative geometry, is defined, with a parameter ε in the centre. When ε is set to zero, the commutative algebra A0 of algebraic functions on an algebraic manifold M is obtained. This A0 is a subalgebra of Cω(M), which is dense if M is compact. The generators of A define an immersion of M into Rn, and M inherits a Poisson structure as the lim...

We define two such pairs (X, i), (Y, j) to be equivalent if there is an isogeny α : X → Y such that if α̃ : End(X) ' End(Y ) is the induced isomorphism, we have α̃ ◦ i = j. It is easy to check that this is an equivalence relation. We write X ∼ Y if (X, i) is equivalent to (Y, j). Let AF be the collection of equivalence classes. We will classify such equivalence classes. Let D be any R-algebra. A ...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

in this paper we study the concept of ph-biatness ofa banach algebra a, where ph is a continuous homomorphism on a.we prove that if ph is a continuous epimorphism on a and a hasa bounded approximate identity and a is ph- biat, then a is ph-amenable. in the case where ph is an isomorphism on a we showthat the ph- amenability of a implies its ph-biatness.

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...