Factorizations of Invertible Operators and ^-theory of C* -algebras

Factorizations of Invertible Operators and K-theory of C-algebras

Let A be a unital C*-algebra. We describe K-skeleton factorizations of all invertible operators on a Hilbert C*-module HA, in particular on H = l 2, with the Fredholm index as an invariant. We then outline the isomorphisms K0(A) ∼= π2k([p]0) ∼= π2k(GL p r(A)) and K1(A) ∼= π2k+1([p]0) ∼= π2k+1(GL p r(A)) for k ≥ 0, where [p]0 denotes the class of all compact perturbations of a projection p in th...

G-frames in Hilbert Modules Over Pro-C*-‎algebras

G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...

Some properties of Invertible Elements in Fuzzy Banach algebras

In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.

Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

On the denseness of the invertible group in uniform Frechet algebras