ISOMORPHIC COPIES IN THE LATTICE E AND ITS SYMMETRIZATION E(*) WITH APPLICATIONS TO ORLICZ-LORENTZ SPACES
主 题: ISOMORPHIC COPIES IN THE LATTICE E AND ITS SYMMETRIZATION E(*) WITH APPLICATIONS TO ORLICZ-LORENTZ SPACES
报告人: Prof. ANNA KAMINSKA (The University of Memphis)
时 间: 2008-12-08 下午 2:40 - 3:40
地 点: 理科一号楼 1490
The paper is devoted to the isomorphic structure of symmetrizations of quasi-Banach
ideal function or sequence lattices. The symmetrization E(*) of a quasi-Banach ideal lattice
E of measurable functions on I = (0, a), 0 < a \\leq \\infty, or I = N, consists of all functions
with decreasing rearrangement belonging to E. For an order continuous E we show that
every subsymmetric basic sequence in E(*) which converges to zero in measure is equivalent
to another one in the cone of positive decreasing elements in E, and conversely. Among
several consequences we show that, provided E is order continuous with Fatou property,
E(*) contains an order isomorphic copy of l^p if and only if either E contains a normalized
l^p-basic sequence which converges to zero in measure, or E(*) contains the function t^{-1/p}.
