Operator Ideals, Orthonormal Systems and Lacunary Sets

✍ Scribed by Franziska Baur

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 429 KB
• Volume: 197
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19991970103

✦ Synopsis

Abstract

Given an orthonormal system B in some L^2^(u) we consider the operator ideals II~B~ and T~B~ of B‐summing and B‐type operators and some related ideals. We characterize by certain weak compactness properties when II~B~ is equal to the operator ideal II~2~ of 2‐summing operators. In lose that B consists of characters of a compact abelian group we characterize when II~B~ coincides with the operator ideal II~γ~ of Gauss‐summing operators and when T~B~ coincides with the operator ideal II~p~ of type‐2 operators. Moreover, we give a necessary and sufficient condition for Fig to contain the operator ideal II~p~ of p‐summing operators (2 < p < ∞) and for T~B~ to contain the operator ideal Γ~p~ of p ‐ factorable operators.