Abstract
In this paper we investigate the solidity (normality) of the sequencespaces c^2_A, l^2_ A, Gamma^2_A and \Lambda^2_A.
Highlights
N.Subramanian and P.Thirunavakarasu abstract: In this paper we investigate the solidity of the sequence spaces c2A, l2A, Λ2A and Γ2A
The vector space of all prime sense double analytic sequences will be denoted by Λ2
The double entire sequences will be denoted by Γ2
Summary
N.Subramanian and P.Thirunavakarasu abstract: In this paper we investigate the solidity (normality) of the sequence spaces c2A, l2A, Λ2A and Γ2A. An FDK-space is a double sequence space endowed with a complete metrizable; locally convex topology under which the coordinate mappings x = (xk) → (xmn)(m, n ∈ N ) are continuous. If X is a sequence space, we give the following definitions: (i)X′ = the continuous dual of X; (ii)Xα = a = (amn) : ; (v)let X beanF K − space ⊃ φ; Xf = f (δmn) : f ∈ X′ ; (vi)XΛ = a = (amn) :msunp |amnxmn|1/m+n < ∞, f oreach x ∈ X ; Xα.Xβ, Xγ are called α − (orKothe − T oeplitz)dual of X, β − (or generalized − Kothe − T oeplitz) dual of X, γ − dual of X, Λ − dual of X respectively.
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