Some New Hilbert Sequence Spaces

Abstract

The main purpose of the present paper is to study of some new Hilbert sequence spaces   ,   and  . New Hilbert sequence spaces  ,   and   consisting all the sequences whose  - transforms are in the spaces  ,  and  , respectively. The new Hilbert sequence spaces  ,   and   that are  - spaces and prove that the spaces  ,   and   are linearly isomorphic to the spaces  ,  and  , respectively. Afterward the bases and α, β and γ duals of these spaces will be given. Finally, matrix the classes   and   have been characterized.

Keywords

• Hilbert sequence spaces,α,β and γ duals and bases of sequence,Matrix mappings

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