Generalized limits and a mean ergodic theorem

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题名:	Generalized limits and a mean ergodic theorem
作者:	Li,SY;Shaw,SY
贡献者:	數學研究所
日期:	1996
上传时间:	2010-06-29 19:39:59 (UTC+8)
出版者:	中央大學
摘要:	For a given linear operator L on l(infinity) with parallel to L parallel to = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on l(infinity) and X = l(infinity), the definition of L-limit reduces to Lorentz's definition of sigma-limit, which is described by means of Banach limits on l(infinity). We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version of the abstract mean ergodic theorem in terms of L-limits. A theorem of Sinclair on the form of linear functionals on a unital normed algebra in terms of states is also generalized.
關聯:	STUDIA MATHEMATICA
显示于类别:	[數學研究所] 期刊論文

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