Results 11 to 20 of about 43 (43)
Calculations on some sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 31, Page 1653-1670, 2004., 2004 We deal with space of sequences generalizing the well‐known spaces w∞p(λ), c∞(λ, μ), replacing the operators C(λ) and Δ(μ) by their transposes. We get generalizations of results concerning the strong matrix domain of an infinite matrix A.
Bruno de Malafosse
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Operators commuting with the shift on sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 43, Page 2273-2278, 2004., 2004 A complete characterization of shift‐invariant operators that are isomorphisms is given in certain sequence spaces. Also given is a sufficient condition for an operator commuting with a shift‐invariant operator to be shift invariant.
J. Prada
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The Orlicz space of entire sequences
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 68, Page 3755-3764, 2004., 2004 Let Γ denote the space of all entire sequences and ∧ the space of all analytic sequences. This paper is devoted to the study of the general properties of Orlicz space ΓM of Γ.
K. Chandrasekhara Rao, N. Subramanian
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On the Banach algebra ℬ(lp(α))
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 60, Page 3187-3203, 2004., 2004 We give some properties of the Banach algebra of bounded operators ℬ(lp(α)) for 1 ≤ p ≤ ∞, where lp(α) = (1/α) −1∗lp. Then we deal with the continued fractions and give some properties of the operator Δh for h > 0 or integer greater than or equal to one mapping lp(α) into itself for p ≥ 1 real. These results extend, among other things, those concerning
Bruno de Malafosse
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International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 28, Page 1783-1801, 2003., 2003 We characterize the spaces sα(Δ), sα∘(Δ), and sα(c)(Δ) and we deal with some sets generalizing the well‐known sets w0(λ), w∞(λ), w(λ), c0(λ), c∞(λ), and c(λ).
Bruno de Malafosse
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Topological duals of some paranormed sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 30, Page 1883-1897, 2003., 2003 Let P = (pk) be a bounded positive sequence and let A = (ank) be an infinite matrix with all ank ≥ 0. For normed spaces E and Ek, the matrix A generates the paranormed sequence spaces [A, P] ∞((Ek)), [A, P] 0((Ek)), and [A, P]((E)), which generalise almost all the well‐known sequence spaces such as c0, c, lp, l∞, and wp.
Nandita Rath
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On β‐dual of vector‐valued sequence spaces of Maddox
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 7, Page 383-392, 2002., 2002 The β‐dual of a vector‐valued sequence space is defined and studied. We show that if an X‐valued sequence space E is a BK‐space having AK property, then the dual space of E and its β‐dual are isometrically isomorphic. We also give characterizations of β‐dual of vector‐valued sequence spaces of Maddox ℓ(X, p), ℓ∞(X, p), c0(X, p), and c(X, p).
Suthep Suantai, Winate Sanhan
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Vector‐valued sequence spaces generated by infinite matrices
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 9, Page 547-560, 2001., 2001 Let A = (ank) be an infinite matrix with all ank ≥ 0 and P a bounded, positive real sequence. For normed spaces E and Ek the matrix A generates paranormed sequence spaces such as [A,P]∞((Ek)), [A,P]0((Ek)), and [A, P](E) which generalize almost all the existing sequence spaces, such as l∞, c0, c, lp, wp, and several others.
Nandita Rath
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On matrix transformations concerning the Nakano vector‐valued sequence space
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 11, Page 671-678, 2001., 2001 We give the matrix characterizations from Nakano vector‐valued sequence space ℓ(X, p) and Fr(X, p) into the sequence spaces Er, ℓ∞, ℓ¯∞(q), bs, and cs, where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that Pk > 1 for all k ∈ ℕ and r ≥ 0.
Suthep Suantai
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International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 1, Page 9-23, 2001., 2001 The paper aims to develop for sequence spaces E a general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe‐Toeplitz duals E×(×∈{α, β}) combined with dualities (E, G), G ⊂ E×, and the SAK‐property (weak sectional convergence).
Johann Boos, Toivo Leiger
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