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Holomorphic and meromorphic properties of the g-Drazin inverse

Koliha J., Rakočević V.

Demonstratio Mathematica

2005

Vol. 38, nr 3

657-666

If A(z) is a function of a complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A (z) g-Drazin invertible, we study the conditions under which the g-Drazin inverse A°(z) is holomorphic and finite-meromorphic. Prom our results we recover a theorem of Steinberg on meromorphic families of compact operators.

Range projections of idempotents in C*-algebras

Koliha J.

Demonstratio Mathematica

2001

Vol. 34, nr 1

91-103

In this paper we study range projections of idempotents m C*-algebras, and use them to obtain a Schur type decomposition that leads to simple proofs of results on Moore-Penrose inverse and norms of idempotents. We analyze the continuity of range projections, obtain a general result on their approximation, and recover a result of Vidav on two projections in a Hilbert space. Several representations of range projections are given.