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

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

Let j/ be a unital C*-algebra. We describe K-skeleton factorizations of all invertible operators on a Hubert C*-module %^ , in particular on «^ = I2 , with the Fredholm index as an invariant. We then outline the isomorphisms K0(s/) =i TC2k([p]0) 3 n2k(GLp(s/)) and Kx(s*) & ä2*+i([Pjo) = n2k+\(GLpr(s?)) for k > 0 , where [p]o 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...

On the denseness of the invertible group in uniform Frechet algebras

The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules

Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...

On the topology of the group of invertible elements – A Survey –

On the topology of the group of invertible elements – A Survey – The topological structure of the group of invertible elements in a unital Banach algebra (regular group for short) has attracted topologists from the very beginning of homotopy theory. Be it for its own sake simply to show the instrumental power of newly invented methods or because there were important applications, the most notab...