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A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations 
International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 681-688
http://dx.doi.org/10.1155/S0161171295000871

A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

B. Choudhary and S. K. Mishra

Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

Received 5 November 1992; Revised 22 September 1993

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we define the sequence spaces S ℓ ∞ ( p ) , S c ( p ) and S c 0 ( p ) and determine the Köthe-Toeplitz duals of S ℓ ∞ ( p ) . We also obtain necessary and sufficient conditions for a matrix A to map S ℓ ∞ ( p ) to ℓ ∞ and investigate some related problems.