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

Crandall, Michael G.; Liggett, Thomas M.

doi:10.1090/S0002-9947-1971-0301592-X

A theorem and a counterexample in the theory of semigroups of nonlinear transformations
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by Michael G. Crandall and Thomas M. Liggett

Trans. Amer. Math. Soc. 160 (1971), 263-278

DOI: https://doi.org/10.1090/S0002-9947-1971-0301592-X

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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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