Almost linear operators and functionals

John R Baxter, R. V. Chacon

Research output: Contribution to journalArticle

Abstract

Let (M) be the bounded continuous functions on a topological space M. "Almost linear" operators (and functionals) on C(M) are defined. Almost linearity does not imply linearity in general. However, it is shown that if M = [O, l] then any almost linear operator (or functional) must be linear. Specifically, if (a)0 implies T(f) 0, (b) T(f + g) = T(f) + T(g) whenever fg = 0, (c) T(f + g) = T(f) + T(g) whenever g is constant, and M[O, l], then T is linear. An application is given to convergence of measur.

Original languageEnglish (US)
Pages (from-to)147-154
Number of pages8
JournalProceedings of the American Mathematical Society
Volume47
Issue number1
DOIs
StatePublished - Jan 1975

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