Analysis Mathematica

, 37:173

On A-invariant mean and A-almost convergence

Article

Abstract

The idea of A-invariant mean and A-almost convergence is due to J. P. Duran [8], which is a generalization of the usual notion of Banach limit and almost convergence. In this paper, we discuss some important properties of this method and prove that the space F(A) of A-almost convergent sequences is a BK space with ‖ · ‖, and also show that it is a nonseparable closed subspace of the space l of bounded sequences.

Об A-инвариантных средних и A-почти сходимости

Резуме

Идея A-инвариантных средних и A-почти сходимости принадлежит Дж. П. Дурану [8] и является обобщением принятых понятий Банахова предела и почти сходимости. В настоящей работе обсуждаются некоторые важные свойства этого метода и устанавливается, что пространство F(A)A-почти сходящихся после-довательностей является BK пространством с нормой ‖ · ‖, а также что оно есть несепарабельное эамкнутое подпространство пространства ограниченных последовательностей.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

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