Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces
نویسندگان
چکیده
منابع مشابه
Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces
and Applied Analysis 3 Lemma 1.4 see 2 . Let X ⊃ φ be a BK-space and Y any of the spaces c0, c, or ∞. If A ∈ X,Y , then ‖LA‖ ‖A‖ X, ∞ sup n ‖An‖X < ∞, 1.4 where ‖A‖ X, ∞ denotes the operator norm for the matrix A ∈ X, ∞ . Sargent 3 defined the following sequence spaces. Let C denote the space whose elements are finite sets of distinct positive integers. Given any element σ of C, we denote by c ...
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15 صفحه اولOn Some Bk Spaces
where B=(bn)n≥1 is a one-columnmatrix andX the unknown, see [2, 3, 5, 6, 7, 9]. Equation (1.2) can be written in the form AX = B, where AX = (An(X))n≥1. In this paper, we will also consider A as an operator from a sequence space into another sequence space. A Banach space E of complex sequences with the norm ‖‖E is a BK space if each projection Pn : X → PnX is continuous. A BK space E is said t...
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We give a survey of the known results concerning the sets c0(Λ), c(Λ) and c∞(Λ) including their basic topological properties, their first and second dual spaces, and the characterizations of matrix transformations from them into the spaces l∞, c and c0. Furthermore, we establish some new results such as the representations of the general bounded linear operators from c(Λ) into the spaces l∞, c ...
متن کاملMeasure of noncompactness of operators and matrices on the spaces c and c0
whenever the series are convergent for all n≥ 1. For any given subsets X , Y of s, we will say that the operator represented by the infinite matrix A = (anm)n,m≥1 maps X into Y that is A∈ (X ,Y), if (i) the series defined by An(x)= ∑∞ m=1 anmxm are convergent for all n≥ 1 and for all x ∈ X ; (ii) Ax ∈ Y for all x ∈ X . If c ⊂ cA = {x : Ax ∈ c},A is conservative. Well-known necessary and suffici...
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ژورنال
عنوان ژورنال: Journal of Function Spaces
سال: 2014
ISSN: 2314-8896,2314-8888
DOI: 10.1155/2014/196489