Affiliation:
1. Basic Science Department, College of Science and Theoretical Studies , Saudi Electronic University-Riyadh , Kingdom of Saudi Arabia
Abstract
Abstract
In this paper, we introduce the generalized spaces of the form ℋ(f, g, Δ
n
m
), where ℋ represents one of the spaces ℓ∞, c or c
0.The köthe duals corresponding to these spaces will be computed and construction of the Schauder bases for ℋ ∈ {c, c
0} will be given. Also, some matrix characterizations concerning these spaces will be computed. Moreover, the characterization of some classes of compact operators on the spaces ℓ∞(f, g, Δ
n
m
)and c
0(f, g, Δ
n
m
)by employing the Hausdorff measure of non-compactness will be determined.
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