On Purely Real Lie Algebras of Skew-Adjoint Operators

Select Volume / Issue:

• Volume 3 Issue 2, March, 2015

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 [Bibtex]