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M-operators on partially ordered Banach spaces
Published in Tusi Mathematical Research Group (TMRG)
Volume: 4
Issue: 2
Pages: 481 - 496
For a matrix A ∈ ℝn × 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. © 2019 by the Tusi Mathematical Research Group.
About the journal
JournalAdvances in Operator Theory
PublisherTusi Mathematical Research Group (TMRG)
Open AccessYes