The Hausdorff measure of noncompactness of matrix operators on some BK spaces
نویسندگان
چکیده
منابع مشابه
some properties of fuzzy hilbert spaces and norm of operators
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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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In this paper, we derive some identities for the Hausdorff measures of noncompactness of certain matrix operators on the sequence spaces X(r,s) of generalized means. Further, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for such operators to be compact. Mathematics subject classification (2010): 46B15, 46B45, 46B50.
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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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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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ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2011
ISSN: 1846-3886
DOI: 10.7153/oam-05-35