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On A-invariant mean and A-almost convergence

Об A-инвариантных средних и A-почти сходимости

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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.

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 ℓ ∞ ограниченных последовательностей.

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  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen

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  1. M. Mursaleen
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Correspondence to M. Mursaleen.

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Mursaleen, M. On A-invariant mean and A-almost convergence. Anal Math 37, 173–180 (2011). https://doi.org/10.1007/s10476-011-0302-x

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