On the uniform Kadec-Klee property with respect to convergence in measure

Journal of the Australian Mathematical Society

F. A. Sukochev¹ 

关键词: primary 46B20;    secondary 46E30;    46L50;   

DOI  :  10.1017/S1446788700037241

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let E(0, ∞) be a separable symmetric function space, let M be a semifinite von Neumann algebra with normal faithful semifinite trace μ, and let E(M, μ) be the symmetric operator space associated with E(0, ∞). If E(0, ∞) has the uniform Kadec-Klee property with respect to convergence in measure then E(M, μ) also has this property. In particular, if LΦ(0, ∞) (ϕ(0, ∞)) is a separable Orlicz (Lorentz) space then LΦ(M, μ) (Λϕ (M, μ)) has the uniform Kadec-Klee property with respect to convergence in measure on sets of finite measure if and only if the norm of E(0, ∞) satisfies G. Birkhoff's condition of uniform monotonicity.

【 授权许可】

Unknown