A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix $\widehat{\widehat{B}}$

Abstract

This study serves for analysing algebraic and topological characteristics of the sequence spaces X( B(r, s)) constituted by using non-zero real number r and s, where X denotes arbitrary of the classical sequence spaces ∞ , c, c 0 and p (1 < p < ∞) of bounded, convergent, null and absolutely p-summable sequences, respectively and X( B) also is the domain of the matrix B(r, s) in the sequence space X. Briefly, the β -and γ-duals of the space X( B) are computed, and Schauder bases for the spaces c( B), c 0 ( B) and p ( B) are determined, and some algebraic and topological properties of the spaces c 0 ( B), 1 ( B) and p ( B) are studied. Additionally, it is observed that all these spaces have some remarkable features, including the classes (X 1 ( B): X 2 ) and (X 1 ( B) : X 2 ( B)) of infinite matrices which are characterized, in which X 1 ∈ { ∞ , c, c 0 , p , 1 } and X 2 ∈ { ∞ , c, c 0 , 1 }.

Domain of Jordan Totient Matrix in the Space of Almost Convergent Sequences

“…For more on matrix domains and new sequence spaces, see [15][16][17][18][19][20][21][22][23][24][25] Let x = (x j ) ∈ ω and C j be the least convex closed region in complex plane containing x j , x j+1 , x j+2 , . .…”