Complex rotundities and midpoint local uniform rotundity in symmetric spaces of measurable operators

• Autorzy: Małgorzata Marta Czerwińska , Anna Kamińska
• Języki publikacji: EN

Abstrakty

EN

We investigate the relationships between strongly extreme, complex extreme, and complex locally uniformly rotund points of the unit ball of a symmetric function space or a symmetric sequence space E, and of the unit ball of the space E(ℳ,τ) of τ-measurable operators associated to a semifinite von Neumann algebra (ℳ,τ) or of the unit ball in the unitary matrix space $C_{E}$. We prove that strongly extreme, complex extreme, and complex locally uniformly rotund points x of the unit ball of the symmetric space E(ℳ,τ) inherit these properties from their singular value function μ(x) in the unit ball of E with additional necessary requirements on x in the case of complex extreme points. We also obtain the full converse statements for the von Neumann algebra ℳ with a faithful, normal, σ-finite trace τ as well as for the unitary matrix space $C_{E}$. Consequently, corresponding results on the global properties such as midpoint local uniform rotundity, complex rotundity and complex local uniform rotundity follow.

Kategorie tematyczne

• 47L20: Operator ideals
• 46B20: Geometry and structure of normed linear spaces
• 47L05: Linear spaces of operators
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 201
• Numer: 3
• Strony: 253-285

Daty

wydano

2010

Twórcy

autor

Małgorzata Marta Czerwińska

• Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, U.S.A.

autor

Anna Kamińska

• Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152

Identyfikatory

DOI

10.4064/sm201-3-3