KFU. Card publication. Automorphisms of spectral lattices of positive contractions on von Neumann Albebras

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FEDERAL UNIVERSITY

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AUTOMORPHISMS OF SPECTRAL LATTICES OF POSITIVE CONTRACTIONS ON VON NEUMANN ALBEBRAS

Form of presentation

Articles in international journals and collections

Year of publication

2014

Authors, employees of KFU

Turilova Ekaterina Aleksandrovna, author

Bibliographic description in the original language

Turilova E., Automorphisms of spectral lattices of positive contractions on von Neumann Albebras// Lobachevskii J. of Math. - V.35. - N.4. - P. 354 – 358

Annotation

We show that any spectral lattice orthoautomorphism of the structure of positive contractions on a von Neumann algebra, endowed with the spectral order and orthogonality relation, that preserves scalar operators is a composition of function calculus with natural transformation of spectral resolutions given by an orthoautomorphism of the projection lattice. In case of von Neumann algebras without Type I2 direct summand any such a map is a composition of function calculus with Jordan ∗-automorphism. This result is a parallel to famous Dye?s theorem and generalizes so far known results on preservers of the spectral order on matrices and operators. Moreover general spectral lattice automorphism are studied.

Keywords

preservers of spectral order, von Neumann algebras, Jordan ∗-automorphisms

The name of the journal

Lobachevski Journ. of Mathematics

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=89242&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Turilova Ekaterina Aleksandrovna	ru_RU
dc.date.accessioned	2014-01-01T00:00:00Z	ru_RU
dc.date.available	2014-01-01T00:00:00Z	ru_RU
dc.date.issued	2014	ru_RU
dc.identifier.citation	Turilova E., Automorphisms of spectral lattices of positive contractions on von Neumann Albebras// Lobachevskii J. of Math. - V.35. - N.4. - P. 354 – 358	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=89242&p_lang=2	ru_RU
dc.description.abstract	Lobachevski Journ. of Mathematics	ru_RU
dc.description.abstract	We show that any spectral lattice orthoautomorphism of the structure of positive contractions on a von Neumann algebra, endowed with the spectral order and orthogonality relation, that preserves scalar operators is a composition of function calculus with natural transformation of spectral resolutions given by an orthoautomorphism of the projection lattice. In case of von Neumann algebras without Type I2 direct summand any such a map is a composition of function calculus with Jordan ∗-automorphism. This result is a parallel to famous Dye?s theorem and generalizes so far known results on preservers of the spectral order on matrices and operators. Moreover general spectral lattice automorphism are studied.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	preservers of spectral order	ru_RU
dc.subject	von Neumann algebras	ru_RU
dc.subject	Jordan ∗-automorphisms	ru_RU
dc.title	Automorphisms of spectral lattices of positive contractions on von Neumann Albebras	ru_RU
dc.type	Articles in international journals and collections	ru_RU