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On the spaces of Cesàro absolutely p ‐summable, null, and convergent sequences
Author(s) -
Roopaei Hadi,
Başar Feyzi
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6973
Subject(s) - mathematics , dual polyhedron , combinatorics , sequence (biology) , order (exchange) , limit of a sequence , space (punctuation) , pure mathematics , mathematical analysis , genetics , biology , linguistics , philosophy , finance , limit (mathematics) , economics
In this paper, we investigate some properties of the domains c 0 ( C n ) , c ( C n ) , and ℓ p ( C n ) with 0 < p < 1 of the Cesàro matrix of order n in the classical spaces c 0 , c , and ℓ p of null, convergent, and absolutely p ‐summable 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 ( C n ) to the spaces ℓ ∞ , c , and c 0 and from a normed sequence spaces to the sequence spaces c 0 ( C n ) , c ( C n ) , and ℓ p ( C n ) . Moreover, we compute the lower bound of operators from ℓ p into ℓ p ( C n ) , from ℓ p ( C n ) into ℓ p and from ℓ p ( C n ) into itself.