On Purely Real Lie Algebras of Skew-Adjoint Operators

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Year:
2015
Type of Publication:
Article
Keywords:
Real Lie Algebra, Real Von Neumann Algebra, Von Neumann Algebra
Authors:
Arzikulov F.; Mamatohunova Yu.
Journal:
IJISM
Volume:
3
Number:
5
Pages:
105-108
Month:
March
ISSN:
2347-9051
Abstract:
In the given paper we investigate a real von Neumann algebra R on a Hilbert space such that R ∩ iR = {0} and a real Lie algebra L of skew-adjoint operators on a Hilbert space H such that R(L) ∩ iR(L) = {0} for the real *-algebra R(L), generated by L in B(H). These algebras are called a purely real von Neumann algebra and a purely real Lie algebra respectively. An analog of Gelfand-Naumark theorem for ultraweakly closed purely real Lie algebras of skew-adjoint operators on a Hilbert space is proved. Also, it is proved that the enveloping C* -algebra of such Lie algebra is a von Neumann algebra if this Lie algebra is reversible and it is given a condition in which a purely real Lie algebra of skew-adjoint operators is reversible
Full text: IJISM-357_Final.pdf

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