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On the factorable spaces of absolutelyp-summable, null, convergent, and bounded sequences
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AbstractLetFdenote the factorable matrix andX∈ {ℓp,c0,c,ℓ∞}. In this study, we introduce the domainsX(F) of the factorable matrix in the spacesX. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spacesX(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓp(F),ℓ∞), (ℓp(F),f) and (X,Y(F)) of matrix transformations, whereYdenotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrixFand derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrixF. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.
Title: On the factorable spaces of absolutelyp-summable, null, convergent, and bounded sequences
Description:
AbstractLetFdenote the factorable matrix andX∈ {ℓp,c0,c,ℓ∞}.
In this study, we introduce the domainsX(F) of the factorable matrix in the spacesX.
Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spacesX(F).
We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓp(F),ℓ∞), (ℓp(F),f) and (X,Y(F)) of matrix transformations, whereYdenotes any given sequence space.
Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrixFand derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix.
Additionally, we investigate the norm of operators on the domain of the matrixF.
Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.
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