()上的线性插值和初等算子

Science in China Series A-Mathematics, Physics, Astronomy & Technological Science Pub Date : 1993-09-20 DOI:10.1360/YA1993-36-9-1025

H. Jin-chuan

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引用次数: 6

摘要

设为巴拿赫空间。本文给出了()上的初等算子秩有限或秩1的充要条件;给出了()上的抽象线性映射为有限秩初等算子的刻画，并证明了有限多个初等算子△1，…，△k的线性插值虽然可能不是△I的线性组合，但仍然是一个初等算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Linear Interpolation and the Elementary Operators on ()

Let be a Banach space.In this paper the sufficient and necessary condi- tions for an elementary operator on () to be of finite rank or of rank one are obtained; a characterization of an abstract linear mapping on () to be a finite-rank elementary operator is given;and it is also shown that a linear interpolation of finitely many elemen- tary operators △ 1 ,…,△ k is still an elementary operator though it may not be a linear combi- nation of △ i 's.

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Science in China Series A-Mathematics, Physics, Astronomy & Technological Science

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