Rank Preserving Maps on CSL Algebras

Details Rank Preserving Maps on CSL Algebras Rank Preserving Maps on CSL Algebras

2006-01-11

arxiv.org/abs/math/0601254v2

Mathematics

Operator Algebras

14 pages

Scientific paper

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.

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