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標題: Convergence rates for ergodic theorems of Kido-Takahashi type
作者: Shaw, S.Y.
Li, Y.C.
關鍵字: strongly regular net of linear functionals;A-ergodic net;mean ergodic;theorem;(Co)-semigroup;approximate solutions;linear-operators;banach-spaces;limits;semigroups
Project: Taiwanese Journal of Mathematics
期刊/報告no:: Taiwanese Journal of Mathematics, Volume 12, Issue 6, Page(s) 1543-1559.
Let {T(t); t >= 0} be a uniformly bounded (C(0))-semigroup of operators on a Banach space X with generator A such that all orbits are relatively weakly compact. Let {phi(alpha)} and {psi(alpha)} be two nets of continuous linear functionals on the space C(b)[0, infinity) of all bounded continuous functions on [0,infinity). {phi(alpha)} and {psi(alpha)} determine two nets {A(alpha)}, {B(alpha)} of operators satisfying < A(alpha)x,x*> = phi(alpha)(< T(.)x,x*>) and (B(alpha)x,x*) = psi(alpha)(< T(.)x,x*>) for all x is an element of X and x* is an element of X*. Under suitable conditions on {phi(alpha)} and {psi(alpha)}, this paper discusses: 1) the convergence of {A(alpha)} and {B(alpha)} in operator norm; 2) rates of convergence of {A(alpha)x} and {A(alpha)y} for each x is an element of X and y is an element of R (A).
ISSN: 1027-5487
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