Basic Properties of Tempered ν-Sequence Spaces

Abstract

In this paper, we will introduce tempered ν-sequence spaces generated by directed preserving generator ν. After building the spaces, we investigate and show tempered ν-sequence spaces are Banach spaces. In addition, we also find that there is an isomorphism between tempered ν-sequence spaces and the classical one. The direct implication is that some tempered ν-sequence spaces have a Schauder basis.

Keywords

• Directed preserving generator
• Tempering sequence
• Banach space
• Schauder basis

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