No abstract

No abstract

We generalize the notion of consistency in invertibility to Banach algebras and prove that the set of all elements consistent in invertibility is an upper semiregularity. In the case of bounded liner operators on a Hilbert space, we give a complete answer when the set of all <em>CI</em> operators will be a regularity. Analogous results are obtained for Fredholm consistent operators.

The aim of this paper is to provide sufficient and necessary conditions under which the linear combination $\alpha A + \beta B$, for given operators $A,B \in {\cal B}({\cal H})$ and $\alpha, \beta \in \mathbb{C}\setminus \lbrace 0 \rbrace$, is injective. Using these results, necessary and sufficient conditions for left (right) invertibility are given. Some special cases will be studied as well.

No abstract