算子的第二类广义BottDuffin逆

J4 ›› 2009, Vol. 44 ›› Issue (6): 14-17.

算子的第二类广义BottDuffin逆

邵春芳

安康学院数学系, 陕西安康 725000

收稿日期:2008-12-24 发布日期:2011-06-03
作者简介:邵春芳(1982-), 女, 硕士, 助教, 研究方向为算子理论与小波分析. Email: scfwzy@yahoo.com.cn
基金资助:
国家自然科学基金资助项目(10871224)；院级专项科研基金资助项目(2008AKXY019)

The second kind of generalized BottDuffin inverse of operators

SHAO Chunfang

Department of Mathematics, Ankang University, Ankang 725000, Shannxi, China

Received:2008-12-24 Published:2011-06-03

摘要/Abstract

摘要：

对矩阵的第二类广义BottDuffin(BD)逆的概念进行推广, 利用算子的｛1｝逆定义无穷维Hilbert空间上有界线性算子A关于一个闭子空间L的第二类广义BottDuffin逆,并运用Hilbert空间上算子分块的技巧分别讨论算子的第二类广义BottDuffin逆的存在性、矩阵表示形式和相关性质。

关键词: 广义BottDuffin逆; ｛1｝逆; MoorePenrose逆; 算子分块

Abstract:

A new generalized BottDuffin(BD) inverse, named the second kind of generalized BottDuffin inverse of bounded linear operator A on an infinite dimensional Hilbert space with respect to a closed subspace L, is defined by using ｛1｝inverse of operators, which is a generalization of the second kind of generalized BottDuffin inverse of matrices. Also, the existence, the representations and some properties of the second kind of generalized BottDuffin inverse are discussed by applying the technique of block operator matrix.

Key words: generalized BottDuffin inverse; ｛1｝inverse; MoorePenrose inverse; block operator

中图分类号:

O1771

. 算子的第二类广义BottDuffin逆[J]. J4, 2009, 44(6): 14-17.

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