ar X iv : m at h / 06 01 25 4 v 2 [ m at h . O A ] 2 M ar 2 00 6 Rank Preserving Maps on CSL Algebras
نویسندگان
چکیده
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.
منابع مشابه
ar X iv : m at h / 06 01 25 4 v 1 [ m at h . O A ] 1 1 Ja n 20 06 Rank Preserving Maps on CSL Algebras
We give a description of a 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 irreducibl...
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