Vol. 51, No. 1, 1974

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Lipschitz spaces

Jerry Alan Johnson

Vol. 51 (1974), No. 1, 177–186
Abstract

If (S,d) is a metric space and 0 < α < 1, Lip (S,dα) is the Banach space of real or complex-valued functions f on S such that f= max(f,faa) < , where faα = sup{|f(s) f(t)|dα(s,t) : st}. The closed subspace of functions f such that limd(s,t)0|f(s) f(t)|dα(s,t) = 0 is denoted by lip (S,dα). The main result is that, when inf std(s,t) = 0 lip (S,dα) contains a complemented subspace isomorphic with c0 and Lip (S,d) contains a subspace isomorphic with l. From the construction, it follows that lip (S,dα) is not isomorphic to a dual space nor is it complemented in Lip (S,dα).

Mathematical Subject Classification 2000
Primary: 46E15
Milestones
Received: 29 November 1972
Revised: 8 March 1973
Published: 1 March 1974
Authors
Jerry Alan Johnson