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 -