On B(m)-difference sequence spaces using generalized means and compact operators

Amit Maji; Parmeshwary Dayal Srivastava

doi:10.1515/anly-2012-1236

Published by Oldenbourg Wissenschaftsverlag August 1, 2014

On B(m)-difference sequence spaces using generalized means and compact operators

Amit Maji and Parmeshwary Dayal Srivastava

From the journal Analysis

https://doi.org/10.1515/anly-2012-1236

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Abstract.

In this paper, sequence spaces X(r,s,t;B(m)) for X∈{l∞,c,c0} are introduced by combining the generalized means and the m-th order generalized difference operator B(m)(u,v). It is shown that these spaces are complete normed linear spaces and the spaces c0(r,s,t;B(m)), c(r,s,t;B(m)) have Schauder bases. Furthermore, the α-, β-, γ-duals of these spaces are computed. The necessary and sufficient conditions for some matrix transformations from X(r,s,t;B(m)) to Y, where X,Y∈{l∞,c,c0}, are also obtained. Finally, some classes of compact operators on the spaces X(r,s,t;B(m)) for X∈{l∞,c,c0} are characterized by using the Hausdorff measure of noncompactness.

Keywords: Difference operator; generalized means; matrix transformation; Hausdorff measure of noncompactness; compact operators

MSC: 46A45; 46B15; 46B50

Funding source: CSIR, New Delhi, Govt. of India

The authors are thankful to the referee for his/her suggestions.

Received: 2013-11-27

Revised: 2014-4-6

Accepted: 2014-5-21

Published Online: 2014-8-1

Published in Print: 2014-8-1

On B(m)-difference sequence spaces using generalized means and compact operators

Abstract.

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