On the Gamma Spaces Including the Spaces of Absolutely p-Summable, Null, Convergent and Bounded Sequences. (27th May 2022) - Roopaei, Hadi; Başar, Feyzi
Abstract: In this paper, we investigate some properties of the domains ℓ p ( Γ n ), c 0 ( Γ n ), c ( Γ n ) and ℓ ∞ ( Γ n ) of the Gamma matrix of order n in the classical spaces ℓ p, c 0, c and ℓ ∞ of absolutely p -summable, null, convergent and bounded sequences, respectively, and compute the α -, β - and γ -duals of these spaces. We characterize the classes of infinite matrices from the space ℓ p ( Γ n ) to the spaces ℓ ∞ and f, and from a normed sequence space to the gamma sequence spaces ℓ p ( Γ n ), c 0 ( Γ n ), c ( Γ n ) and ℓ ∞ ( Γ n ) . Moreover, we introduce the necessary and sufficient conditions for factorizing an operator based on the weighted mean matrices and derive the factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Finally, we emphasize on the lower bound of operators from ℓ p into ℓ p ( Γ n ), from ℓ p ( Γ n ) into ℓ p, from ℓ p ( Γ n ) into itself and from ℓ p into itself.