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Spring 2019 $M$-operators on partially ordered Banach spaces
A. ‎Kalauch, S. ‎Lavanya, K. C. ‎Sivakumar
Adv. Oper. Theory 4(2): 481-496 (Spring 2019). DOI: 10.15352/aot.1806-1383

Abstract

‎For a matrix $A \in \mathbb{R}^{n \times n}$ whose off-diagonal entries are nonpositive‎, ‎there are several well-known properties that are equivalent to $A$ being an invertible $M$-matrix‎. ‎One of them is the positive stability of $A$‎. ‎A generalization of this characterization to partially ordered Banach spaces is considered in this article‎. ‎Relationships with certain other equivalent conditions are derived‎. ‎An important result on singular irreducible $M$-matrices is generalized using the concept of $M$-operators and irreducibility‎. ‎Certain other invertibility conditions of $M$-operators are also investigated‎.

Citation

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A. ‎Kalauch. S. ‎Lavanya. K. C. ‎Sivakumar. "$M$-operators on partially ordered Banach spaces." Adv. Oper. Theory 4 (2) 481 - 496, Spring 2019. https://doi.org/10.15352/aot.1806-1383

Information

Received: 13 June 2018; Accepted: 27 October 2018; Published: Spring 2019
First available in Project Euclid: 1 December 2018

zbMATH: 07009321
MathSciNet: MR3883148
Digital Object Identifier: 10.15352/aot.1806-1383

Subjects:
Primary: 47B60
Secondary: 15B48 , ‎46B40 , 47B65

Keywords: ‎ ‎irreducibility‎ , $M$-operator‎ , invertibility , ‎positive stability ‎

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 2 • Spring 2019
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