SOME RESULTS RELATED TO THE SEPARABLE QUOTIENT PROBLEM

作     者：钟怀杰 Zhong Huaijie(Dept. of Math., Fujian Normal University, Fuzhou 350007, China.)

作者机构：Dept. of Math. Fujian Normal University Fuzhou 350007 China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：1996年第16卷第3期

页      面：248-256页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 070102[理学-计算数学] 0704[理学-天文学] 0701[理学-数学] 

主　　题：Banach space separable space quotient space bounded linear operator 

摘      要：The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed.