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2013•PositivityOpen access

Real ideals of compact operators of complex factors

Sergio Albeverio, R. A. Dadakhodjaev, A. A. Rakhimov

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Abstract

Real ideals of compact operators for (complex) factors are investigated. A description (up to isomorphisms) of real two-sided ideals of relatively compact operators of a complex W*-factors is given. A relative weak (RW) $$_r$$ convergence in a real Hilbert space is introduced. The classical Hilbert characterization of compactness of operators is extended to the compact operators in semifinite real W*-algebras.

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Real ideals of compact operators for (complex) factors are investigated. A description (up to isomorphisms) of real two-sided ideals of relatively compact operators of a complex W*-factors is given. A relative weak (RW) $$_r$$ convergence in a real Hilbert space is introduced. The classical Hilbert characterization of compactness of operators is extended to the compact operators in semifinite real W*-algebras.

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Available abstract

Real ideals of compact operators for (complex) factors are investigated. A description (up to isomorphisms) of real two-sided ideals of relatively compact operators of a complex W*-factors is given. A relative weak (RW) $$_r$$ convergence in a real Hilbert space is introduced. The classical Hilbert characterization of compactness of operators is extended to the compact operators in semifinite real W*-algebras.

Key concepts: Compact operator on Hilbert space, Operator theory, Mathematics, Nuclear operator, Hilbert space, Pure mathematics, Compact space, Compact operator

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