EXTENSION OF C-ASTERISK-ALGEBRAS AND MOORE-PENROSE STABILITY OF SEQUENCES OF ADDITIVE OPERATORS

An extension (A) over tilde of a C-algebra A by some element m, which has a number of special properties is proposed. These properties allo w us to introduce some suitable operations of addition, multiplication and involution on (A) over tilde after which we are able to study dif ferent kinds of Moore-Penrose invertibility in (A) over tilde. Due to such an approach, we obtain necessary and sufficient conditions of wea k asymptotic Moore-Penrose invertibility for an algebra arising from s pline approximation methods for singular integral equations with conju gation. (C) 1998 Elsevier Science Inc. All rights reserved.