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Rank Preserving Maps on CSL Algebras

Research paper by Jaedeok Kim, Robert L. Moore

Indexed on: 02 Mar '06Published on: 02 Mar '06Published in: Mathematics - Operator Algebras



Abstract

We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps. We also show that a rank preserving map can be implemented by only one type if the corresponding lattice is irreducible. We present some examples of both types of rank preserving map.