Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals

2017/04/06 by Czerwinska, Malgorzata Marta, Kaminska, Anna
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1704.02033

Abstract

This is a survey article of geometric properties of noncommutative symmetric spaces of measurable operators E(M,τ), where M is a semifinite von Neumann algebra with a faithful, normal, semifinite trace τ, and E is a symmetric function space. If E⊂ c₀ is a symmetric sequence space then the analogous properties in the unitary matrix ideals C_E are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss the properties of general singular value function, submajorization in the sense of Hardy, Littlewood and Pólya, Köthe duality, the spaces L_p(M,τ), 1≤ p

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• Banach Envelopes in Symmetric Spaces of Measurable Operators
• Isometric Structure in Noncommutative Symmetric Spaces
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