关于L^p空间(0

STUDY OF ALMOST ISOMETRIC OPERATORS ON THE POSITIVE CONES OF L p SPACES (0< p <∞)

作　　者：詹大鹏[1] 

机构地区：[1]南开大学数学系

出　　处：《南开大学学报（自然科学版）》1999年第2期34-38,共5页Acta Scientiarum Naturalium Universitatis Nankaiensis

摘　　要：证明了在∈ｐ（０，１）∪（２，∞）时，对于实和复的两种情形，若Ｔ∈Ｂ（Ｌｐ（Ω１），Ｌｐ（Ω２））在正锥上几乎等距，则Ｔ在全空间几乎等距．In this paper, it is shown that, under the case of both real and complex, If an operator T∈B( L p (Ω 1), L p (Ω 2)) is almost isometric on the positive cone, where p ∈(0,1)∪(2,∞), then T is almost isometric on the whole space. This paper also discusses the cases when p takes other values.

关 键 词：L^P空间 正锥 几乎等距算子 赋范空间 

分 类 号：O177.3[理学—数学]