On Certain Topological Structures of Product Normed Space Valued Paranormed Space of Summable Sequences
Keywords:
Sequence space, paranormed space, product normed space, GK- sequence spaceAbstract
The aim of this paper is to introduce and study a new vector valued sequence space S( ( Z, || ( . , . ) ||Z ), ?, u ) with terms from a product normed space as a generalization of sequence space studied by Srivastava and Pahari (2011) which is itself the generalization of the familiar absolutely summable sequence space l. We investigate its linear structure with respect to the co-ordinate wise vector operation and explore the conditions in terms of different u and ? so that a class is contained in another class of same kind and thereby derive the conditions of their equality. Finally we investigate the paranormed structure of S ( ( Z, || (. , . ) ||Z ), ?, u ) by endowing it with a suitable natural paranorm.
Journal of Institute of Science and Technology, 2014, 19(1): 25-29
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