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

Access to Document

10.1002/mana.201300252

Cite this

@article{03d13dd3ae854b7c8bb3fe73fd894c84,

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

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.",

keywords = "Functions of non-commuting operators, Operator equation, Positivity of solutions",

author = "Michael Gil'",

note = "Publisher Copyright: {\textcopyright} 2016 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim.",

year = "2016",

month = jun,

day = "1",

doi = "10.1002/mana.201300252",

language = "English",

volume = "289",

pages = "974--981",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-VCH Verlag",

number = "8-9",

}

TY - JOUR

T1 - Two-sided estimates and positivity conditions for solutions of linear operator equations in a Banach lattice

AU - Gil', Michael

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

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.

KW - Functions of non-commuting operators

KW - Operator equation

KW - Positivity of solutions

UR - https://www.scopus.com/pages/publications/84954305767

U2 - 10.1002/mana.201300252

DO - 10.1002/mana.201300252

M3 - Article

AN - SCOPUS:84954305767

SN - 0025-584X

VL - 289

SP - 974

EP - 981

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 8-9

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this