A New Sequence Space bₚ^r, s (Q)

Key Points

• The aim is to introduce and characterize a new sequence space defined as b_p^{r,s}(Q).
• Constructed the sequence space using quadruple band matrix and binomial matrix.
• Demonstrated linear isomorphism between b_p^{r,s}(Q) and classical space lp.
• Establish the Schauder basis of the new space.
• Identified the α−, β−, and γ− duals of this space.
• Characterized certain matrix classes related to b_p^{r,s}(Q).
• Proved that the space b_p^{r,s}(Q) is linearly isomorphic to the classical lp space.
• Established several inclusion relations involving the new sequence space.
• Determined the Schauder basis for b_p^{r,s}(Q).
• Characterized the duals of the space, enhancing understanding of its structure.
• Identified unique matrix classes associated with b_p^{r,s}(Q).

Abstract