数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (2): 254-260.
丁义明
DING Yi-Ming
摘要：
Let (X,, μ) be a −finite measure space, P : L1 ! L1 be a Markov operator,and Qt =P1 n=0 qn(t)Pn, where {qn(t)} be a sequence satisfying:
i) qn(t) 0 and P1 n=0 qn(t) = 1 for all t > 0; ii) lim t!1 (q0(t) +P1 n=1 |qn(t) − qn−1(t)|) = 0. f 2 L1, it is proved that Qt(f) convergent strongly to a fixed point of P as t ! 0 if and only if {Qt(f)}t>0 is precompact. Qt(f) is convergent if and only if the ergodic mean operator An(f) is convergent, and they have the same limit. If P is a double stochastic operator then lim t!1 Qtf = E(f|0) for all f 2 L1, where 0 is the invariant -algebra of P. Some related results are also given.
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