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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.

Hyperidentities and hypersubstitutions in the variety of symmetric, idempotent, entropic groupoids

Arworn Sr., Denecke K.

Demonstratio Mathematica

1999

Vol. 32, nr 4

677-686

In this paper we determine the structure of the groupoid of normal form hypersubstitutions with respect to the variety of symmetric, idempotent, entropic groupoids, describe the monoid of all proper hypersubstitutions, and ask which identities are satisfied as hyperidentities.