TY - JOUR

T1 - Almost linear operators and functionals

AU - Baxter, John R

AU - Chacon, R. V.

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1975/1

Y1 - 1975/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84966228789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966228789&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1975-0352380-9

DO - 10.1090/S0002-9939-1975-0352380-9

M3 - Article

AN - SCOPUS:84966228789

SN - 0002-9939

VL - 47

SP - 147

EP - 154

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -