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 ?, ? and ? duals of these spaces will be given. Finally, matrix the classes and have been characterized.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 ?, ? and ? duals of these spaces will be given. Finally, matrix the classes and have been characterized.