Semi-Fredholm theory in $$C^{*}$$-algebras

Fredholm Modules over Certain Group C*-algebras

Motivated by the search for new examples of “noncommutative manifolds”, we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consider are the infinite dihedral group Z×σZ2 and the semidirect product group Z×σZ. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.

On C-algebras and K-theory for Infinite-dimensional Fredholm Manifolds

Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space E with Riemannian metric g. Given an augmented Fredholm filtration F of M by finite-dimensional submanifolds {Mn}∞n=k, we associate to the triple (M, g,F) a non-commutative direct limit C-algebra A(M, g,F) = lim −→ A(Mn) that can play the role of the algebra of functions vanishing at infinity on the ...

The Fredholm Index for Elements of Toeplitz-composition C*-algebras

On semi maximal filters in BL-algebras

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

Isomorphisms in unital $C^*$-algebras

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...