Banach空间子空间的维数及其应用

Dimension of the Subspaces of a Banach Space and Its Application

对 Banach空间的任意闭子空间 ,引入一种广义维数及其加法与减法 ,并使之全序化 .发现了可列个无限维数∞*<∞n<∞m,其中 m,n为整数且 n>m.由此对 Banach空间上的任意有界线性算子定义了广义指标 ,并讨论了非线性映射的秩定理 .

A generalized dimension and its addition and subtraction are introduced for any closed subspace of a Banach space, and the numerable dimension ∞ *<∞ n<∞ m is found where m and n are integers and n>m. The generalized index of bounded operator is defined thereafter and the rank theorem of nonlinear map is also discussed.