Monotonicity and complex convexity in Banach lattices |
| |
Authors: | Han Ju Lee |
| |
Institution: | Division of Applied Mathematics, KAIST, 373-1, Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of Korea |
| |
Abstract: | The goal of this article is to study the relations among monotonicity properties of real Banach lattices and the corresponding convexity properties in the complex Banach lattices. We introduce the moduli of monotonicity of Banach lattices. We show that a Banach lattice E is uniformly monotone if and only if its complexification EC is uniformly complex convex. We also prove that a uniformly monotone Banach lattice has finite cotype. In particular, we show that a Banach lattice is of cotype q for some 2?q<∞ if and only if there is an equivalent lattice norm under which it is uniformly monotone and its complexification is q-uniformly PL-convex. We also show that a real Köthe function space E is strictly (respectively uniformly) monotone and a complex Banach space X is strictly (respectively uniformly) complex convex if and only if Köthe-Bochner function space E(X) is strictly (respectively uniformly) complex convex. |
| |
Keywords: | Banach lattice Monotone Uniformly monotone Complex convex Modulus of complex convexity Modulus of monotonicity Uniformly PL-convex Concavity Cotype Lower estimate Kö the-Bochner function spaces |
本文献已被 ScienceDirect 等数据库收录! |
|