On moment sequences of operators

Reports on Mathematical Physics, 2000

AIP Conference Proceedings, 2012

We reduce the spaces a r 0 , a r c , a r 0 (Δ) and a r c (Δ) and simplify their dual spaces and the characterisations of matrix transformations on them. We also obtain an estimate and a formula for the Hausdorff measure of noncompactness of some matrix operators on the spaces a r 0 and a r c , and the corresponding characterisations of compact matrix operators.

Bulletin of the Belgian Mathematical Society - Simon Stevin, 1999

J. K. Brooks and P. W. Lewis have established that if E and E * have RNP, then in M (Σ, E), m n converges weakly to m if and only if m n (A) converges weakly to m(A) for each A ∈ Σ. Assuming the existence of a special kind of lifting, N. Randrianantoanina and E. Saab have shown an analogous result if E is a dual space. Here we show that for the space M (P(N), E) where E * is a Grothendieck space or E is a Mazur space, this kind of weak convergence is valid. Also some applications for subspaces of L(E, F) similar to the results of N. Kalton and W. Ruess are given.

Annals of Functional Analysis, 2011

In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v, ∆ (m)), where X is one of the spaces ∞ , c or c 0. Also, we determine the α-, β-and γ-duals of those spaces and construct their Schauder bases for X ∈ {c, c 0 }. Morever, we give the characterization of the matrix mappings on the spaces X(u, v, ∆ m) for X ∈ { ∞ , c, c 0 }. Finally, we characterize some classes of compact operators on the spaces ∞ (u, v, ∆ m) and c 0 (u, v, ∆ m) by using the Hausdorff measure of noncompactness.

Computers & Mathematics with Applications, 2011

where (K n ) n is a kernel satisfying suitable assumptions and f belongs to L p -spaces. These operators were extensively studied by Butzer and Jansche in in connection with the Mellin transform theory. Among the above operators, an important example is given by the moment (or average) operator whose kernel is given by (see Section 2)

Hacettepe Journal of Mathematics and Statistics, 2018

Let us recall that an operator T : E → F, between two Banach lattices, is said to be weak* Dunford-Pettis (resp. weak almost limited) if fn (T xn) → 0 whenever (xn) converges weakly to 0 in E and (fn) converges weak* to 0 in F (resp. fn (T xn) → 0 for all weakly null sequences (xn) ⊂ E and all weak* null sequences (fn) ⊂ F with pairwise disjoint terms). In this note, we state some sufficient conditions for an operator R : G → E(resp. S : F → G), between Banach lattices, under which the product T R (resp. ST) is weak* Dunford-Pettis whenever T : E → F is an order bounded weak almost limited operator. As a consequence, we establish the coincidence of the above two classes of operators on order bounded operators, under a suitable lattice operations' sequential continuity of the spaces (resp. their duals) between which the operators are defined. We also look at the order structure of the vector space of weak almost limited operators between Banach lattices.

Proceedings of the London Mathematical Society, 1979

2018

Let w be the set of all real or complex sequences and l∞, c and c0 respectively, be the Banach spaces of bounded, convergent and null sequences x = (xk), normed by ‖x‖ = sup k |xk|, where k ∈ N. Let X and Y be two sequence spaces and A = (aik) be an infinite matrix of real or complex numbers aik, where i, k ∈ N. Then we say that A defines a matrix mapping from X into Y if for every sequence x = (xi) ∈ X, the sequence Ax = {Ai(x)}, the A-transform of x, is in Y , where

Canadian Journal of Mathematics

In this work, we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) the doubly truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier operators of limited smoothness. The a.e. convergence is deduced from the $L^2\times \cdots \times L^2\to L^{2/m}$ boundedness of the associated maximal multilinear operators.

Journal of Inequalities and Applications, 2011

Journal of Functional Analysis, 2008

Let β ≡ β (2n) = {βi} |i|≤2n denote a d-dimensional real multisequence, let K denote a closed subset of R d , and let P2n := {p ∈ R[x1, . . . , x d ] : deg p ≤ 2n}. Corresponding to β, the Riesz functional L ≡ L β : P2n −→ R is defined by L( aix i ) := aiβi. We say that L is K-positive if whenever p ∈ P2n and p|K ≥ 0, then L(p) ≥ 0. We prove that β admits a K-representing measure if and only if L β admits a K-positive linear extensionL : P2n+2 −→ R. This provides a generalization (from the full moment problem to the truncated moment problem) of the Riesz-Haviland Theorem. We also show that a semialgebraic set solves the truncated moment problem in terms of natural "degree-bounded" positivity conditions if and only if each polynomial strictly positive on that set admits a degree-bounded weighted sum-of-squares representation.

Stochastic Processes and their Applications, 1997

We discuss three forms of convergence in distribution which are stronger than the normal weak convergence. They have the advantage that they are non-topological in nature and are inherited by discontinuous functions of the original random variables-clearly an improvement on 'normal' weak convergence. We give necessary and sufficient conditions for the three types of convergence and go on to give some applications which are very hard to prove in a more restricted setting.

We show that the sequence spaces a r 0 , a r c and a r ∞ are equal to the sets of all sequences whose Cesàro means of order 1 converge to 0, converge and are bounded. As a consequence of this, we are able to considerably simplify the known results and their proofs in , and to add the characterisations of some more classes of matrix transformations.

Proyecciones (Antofagasta)