Generalized limits and a mean ergodic theorem

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/28006

Title:	Generalized limits and a mean ergodic theorem
Authors:	Li,SY;Shaw,SY
Contributors:	數學研究所
Date:	1996
Issue Date:	2010-06-29 19:39:59 (UTC+8)
Publisher:	中央大學
Abstract:	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.
Relation:	STUDIA MATHEMATICA
Appears in Collections:	[Graduate Institute of Mathematics] journal & Dissertation

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