可分商空间

可分商空间 SEPARABLE QUOTIENT SPACES 石峰 Shi Feng 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 考虑无穷维商空间问题，得到一个无穷维Ｂａｎａｃｈ空间Ｘ具有可分的无穷维商空间的几个充分条件．并且还得到：若Ｘ＊含有ｌ１，则或者Ｘ含有ｌ１，或者Ｘ有商空间同构于ｃ０ In this article,we discuss infinite dimensional separable quotient space,get some sufficient conditions about a Banach space has infinite dimensional separable quotient space especially,if X,Y are Bauach spaces,T: X→Y is a bounded liutar operator, R （T） is dense but not close in Y,then,Y has an infinite dimension separable quotient space ,and get that if X * contains l 1 copy, then X has l 1 copy or X has a quotient space which isomorphic to c 0 . 可分商空间 Schauder基 有界线性算子 separable quotient space Schauder basis bounded linear operator O177.3 国家自然科学基金(61672102) 1996-05-01 2021-04-01 5