DSpace Collection: Volume 32, Number 1
http://hdl.handle.net/10525/2498
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An extension of Lorentz's almost convergence and applications in Banach spaces
http://hdl.handle.net/10525/2509
Title: An extension of Lorentz's almost convergence and applications in Banach spaces<br/><br/>Authors: Mercourakis, S.; Vassiliadis, G.<br/><br/>Abstract: We investigate an extension of the almost convergence of G. G. Lorentz requiring that the means of a bounded sequence converge uniformly on a subset M of N. We also present examples of sequences α∈ l∞(N) whose sequences of translates (Tn α)n≥ 0 (where T is the left-shift operator on l∞(N)) satisfy: (a) Tn α, n ≥ 0 generates a subspace E(α) of l∞(N) that is isomorphically embedded into c0 while α is not almost convergent. (b) Tn α, n ≥ 0 admits an l1-subsequence and a nontrivial weakly Cauchy subsequence while a is almost convergent. Finally we show that, in the sense of measure, for almost all real sequences taking values in a compact set K ⊆ R (with at least two points), the sequence (Tn α)n ≥ 0 is equivalent in the supremum norm to the usual l1-basis and (hence) not almost convergent.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 40C99, 46B99.On Local Uniform Topological Algebras
http://hdl.handle.net/10525/2506
Title: On Local Uniform Topological Algebras<br/><br/>Authors: Oukhouya, Ali<br/><br/>Abstract: Every unital "combinatorially regular" commutative uniform complete locally m-convex algebra is local.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.Criterion of Normality of the Completely Regular Topology of Separate Continuity
http://hdl.handle.net/10525/2504
Title: Criterion of Normality of the Completely Regular Topology of Separate Continuity<br/><br/>Authors: Grinshpon, Yakov S.<br/><br/>Abstract: For given completely regular topological spaces X and Y, there is a completely regular spaceX ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuousif and only if f : X ~⊗ Y→ Z is continuous.We prove a necessary condition of normality, a sufficient condition of collectionwise normality, and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.<br/><br/>Description: 2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.Little G. T. for lp-lattice summing operators
http://hdl.handle.net/10525/2502
Title: Little G. T. for lp-lattice summing operators<br/><br/>Authors: Mezrag, Lahcène<br/><br/>Abstract: In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case.<br/><br/>Description: 2000 Mathematics Subject Classification: 46B28, 47D15.On the Range and the Kernel of Derivations
http://hdl.handle.net/10525/2501
Title: On the Range and the Kernel of Derivations<br/><br/>Authors: Bouali, Said; Bouhafsi, Youssef<br/><br/>Abstract: Let H be a separable infinite dimensional complex Hilbert space and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A ∈ L(H), the derivation δA : L(H)→ L(H) is defined by δA(X) = AX-XA. In this paper we prove that if A is an n-multicyclic hyponormal operator and T is hyponormal such that AT = TA, then || δA(X)+T|| ≥ ||T|| for all X ∈ L(H). We establish the same inequality if A is a finite operator and commutes with normal operator T. Some related results are also given.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.Piecewise Convex Curves and their Integral Representation
http://hdl.handle.net/10525/2500
Title: Piecewise Convex Curves and their Integral Representation<br/><br/>Authors: Nedelcheva, M. D.<br/><br/>Abstract: A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the Riemann-Stieltjes integral with respect to an increasing, nonnegative and continuous from the right function s+. Further it is shown that the obtained representation relates to the support function of the set FG. Concerning the reverse question, namely what can be said for the curves that admit such representation, it is shown that they are exactly the curves that can be decomposed into finitely many convex arcs. This result suggests the name piecewise convex curves. In particular, the class of piecewise convex curves contains the convex curves being boundary sets of convex figures, therefore the results from the paper can be used as a tool for studying convex curves.<br/><br/>Description: 2000 Mathematics Subject Classification: 52A10.Domaine Numérique du produit AB avec A normal
http://hdl.handle.net/10525/2499
Title: Domaine Numérique du produit AB avec A normal<br/><br/>Authors: Kaadoud, Mohamed Chraïbi<br/><br/>Abstract: Let A, B be two linear operators on a complex Hilbert space H. We extend a Bouldin's result (1969) conserning W(AB) - the numerical range of the product AB. We show, when AB = BA and A is normal, than W(AB).<br/><br/>Description: 2000 Mathematics Subject Classification: 18B30, 47A12.