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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.