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Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1018-1024.

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Nonnegative Generalized Inverses of Linear Operators

Xianhua Song()

College of Mathematics and Statistics, Qinghai Normal University, Xining 810016

Received:2017-06-14 Online:2019-10-26 Published:2019-11-08
Supported by:
the Qinghai Normal University School-Level Project: Generalized Inverse Study of Linear Operators(2018zr004)

Abstract

Abstract:

Let B(H) be the set of all bounded linear operators on a complex Hilbert space H. Using the block operator technique, some necessary and suffcient conditions for the existence of nonnegative {1, 3}-, {1, 4}-, {1, 3, 4}-inverses for an operator A∈ B(H) with closed range is given in this paper, and these sets are completely descibed. Moreover, it is showed that the existence of nonnegative {1, 3}-, {1, 4}-inverse of an operator A is equivalent to existence of its nonnegative {1, 2, 3}-, {1, 2, 4}-inverse, respectively.

Key words: Nonnegative generalized inverse, Moore-Penrose inverse, Positive operator

CLC Number:

O177.1

Xianhua Song. Nonnegative Generalized Inverses of Linear Operators[J].Acta mathematica scientia,Series A, 2019, 39(5): 1018-1024.

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Nonnegative Generalized Inverses of Linear Operators

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