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Some remarks on the Barrier Lemma and 𝒦‐monotonicity
Author(s) -
Marek I.
Publication year - 1995
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680020505
Subject(s) - mathematics , linear operators , lemma (botany) , monotonic function , bounded function , monotone polygon , banach space , operator theory , pure mathematics , finite rank operator , bounded operator , bounded inverse theorem , discrete mathematics , mathematical analysis , ecology , geometry , poaceae , biology
An abstract version of the well known Barrier Lemma is presented and some of its generalizations are shown for bounded linear and some unbounded densely defined linear monotone operators in some partially ordered Banach spaces. ‐monotonicity of generally unbounded operators is characterized. Some applications of constructing error bounds for approximately solving equations governed by bounded linear operators are established.