Two-sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice

Michael Gil'

doi:10.1002/mana.201300252

Two-sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice

Michael Gil'

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let A and Ã be bounded linear operators in a Banach lattice B, and M be a positive operator in B. The paper deals with the equation ∑_j=0^m1∑_k=0^m2c_jkA^jXÃ^k = M, where X should be found and c_jk are real numbers. Two-sided estimates and positivity conditions for a solution of that equation are established. The illustrative examples are also presented.

Original language	English
Pages (from-to)	974-981
Number of pages	8
Journal	Mathematische Nachrichten
Volume	289
Issue number	8-9
DOIs	https://doi.org/10.1002/mana.201300252
State	Published - 1 Jun 2016

Keywords

Functions of non-commuting operators
Operator equation
Positivity of solutions

ASJC Scopus subject areas

General Mathematics

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10.1002/mana.201300252

Cite this

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abstract = "Let A and {\~A} be bounded linear operators in a Banach lattice B, and M be a positive operator in B. The paper deals with the equation ∑j=0m1∑k=0m2cjkAjX{\~A}k = M, where X should be found and cjk are real numbers. Two-sided estimates and positivity conditions for a solution of that equation are established. The illustrative examples are also presented.",

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AB - Let A and Ã be bounded linear operators in a Banach lattice B, and M be a positive operator in B. The paper deals with the equation ∑j=0m1∑k=0m2cjkAjXÃk = M, where X should be found and cjk are real numbers. Two-sided estimates and positivity conditions for a solution of that equation are established. The illustrative examples are also presented.

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Two-sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice

Abstract

Keywords

ASJC Scopus subject areas

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