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- W2001180708 abstract "Let G be a locally compact semigroup (jointly continuous semigroup operation), M(G) the algebra of all bounded regular Borel measures on G (with convolution as multiplication), E a separated locally convex space and S a compact convex subset of E. We show that there is a left invariant mean on the space LUC(G) of all bounded left uniformly continuous functions on G iff G has the following fixed point property: For any bilinear mapping T: M(G) x E E (denoted by (,a, s) -* T,,(s)) such that (a) T,,(S) C S for any It > O, Il,ull = 1, (b) TMu*v = Tu ? Tv for any It, vCM(G), (c) T,u:S-S is continuous for any ,u _ O, I,ul = 1, and (d) It TMu(s) is continuous for each s C S when M(G) has the topology induced by the seminorms pf(,U) = Sf f dyl, f C LUC(G), there is some so C S such that TM(so) = so for any I > 0, Ilufl = 1." @default.
- W2001180708 created "2016-06-24" @default.
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- W2001180708 date "1972-01-01" @default.
- W2001180708 modified "2023-09-23" @default.
- W2001180708 title "Invariant means on locally compact semigroups" @default.
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- W2001180708 doi "https://doi.org/10.1090/s0002-9939-1972-0289708-1" @default.
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