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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A theorem and a counterexample in the theory of semigroups of nonlinear transformations


Authors: Michael G. Crandall and Thomas M. Liggett
Journal: Trans. Amer. Math. Soc. 160 (1971), 263-278
MSC: Primary 47H99; Secondary 47D05
DOI: https://doi.org/10.1090/S0002-9947-1971-0301592-X
MathSciNet review: 0301592
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Abstract: This paper studies the basic method in current use for constructively obtaining a generator from a given semigroup of nonlinear transformations on a Banach space. The method is shown to succeed in real two-dimensional Banach spaces and to fail in a particular three-dimensional example. Other results of independent interest are obtained. For example, it is shown that the concepts of ``maximal accretive'' and ``hyperaccretive'' (equivalently, $ m$-accretive or hypermaximal accretive) coincide in $ {R^n}$ with the maximum norm.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0301592-X
Keywords: Nonlinear semigroups, generator, accretive, extension theorem
Article copyright: © Copyright 1971 American Mathematical Society