A Theorem and a Counterexample in The Theory of Semigroups of Nonlinear Transformations

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.

Locations

• Transactions of the American Mathematical Society - View - PDF