Asymptotic Periodicity of the Iterates of Positivity Preserving Operators
نویسنده
چکیده
Assume that (AI) X is a real Banach space. (A2) X+ is a closed subset of X with the following properties: (i) if xe X+, y € X+, a e [0, oo) then x + y & X+ and ax € X+; (ii) there exists Mo € (0, oo) such that for each x € X there exist x+ e X+ and x_ 6 X+ which satisfy _=_+-__, ||_+|| < Mo||x||, ||x_||<Mo||x|| and if x = j/+ — j/_ for some y+ 6 X+, j/_ _ X+ then y+ — x.|6 X+; (iii) if x e X+, y e X+ then ||x|| < ||x + y\\. (A3) B is a bounded linear operator on X. (A4) BX+ C X+. (A5) Fq is a nonempty compact subset of X and limn—oo dist(_J"x, Fq) = 0 whenever x 6 X+ and ||x|| = 1. Then Bnx is asymptotically periodic for every x 6 X. This, and other properties of B, are proven in the paper.
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تاریخ انتشار 2010