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Some characterizations of Banach lattices with the Schur property.

Witold Wnuk (1989)

Revista Matemática de la Universidad Complutense de Madrid

This note contains a short proof of the equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces. We also present an operator characterization of the Schur property (Theorem 2) and we notice that Banach lattices which band hereditary l1 coincide with Banach lattices having the Schur property. (This characterization is due to Popa (1977)). Moreover, the paper offers examples of Banach lattices with the positive Schur property and without the Schur property and which...

Some characterizations of order weakly compact operator

Belmesnaoui Aqzzouz, Aziz Elbour (2011)

Mathematica Bohemica

We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.

Some characterizations of ultrabornological spaces

Manuel Valdivia (1974)

Annales de l'institut Fourier

Let U be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let F be an infinite-dimensional Banach space. Then F is the inductive limit of a family of spaces equal to E . The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let Ω be a non-empty open set in the euclidean n -dimensional space R n . Then F is the inductive limit of a family of spaces equal to D ( Ω ) .

Some classes of infinitely differentiable functions

G. S. Balashova (1999)

Mathematica Bohemica

For nonquasianalytical Carleman classes conditions on the sequences { M ^ n } and { M n } are investigated which guarantee the existence of a function in C J { M ^ n } such that u(n)(a) = bn,    bnKn+1Mn,    n = 0,1,...,    aJ. Conditions of coincidence of the sequences { M ^ n } and { M n } are analysed. Some still unknown classes of such sequences are pointed out and a construction of the required function is suggested. The connection of this classical problem with the problem of the existence of a function with given trace at the boundary...

Some classes of multilinear operators on C(K) spaces

Fernando Bombal, Maite Fernández, Ignacio Villanueva (2001)

Studia Mathematica

We obtain a classification of projective tensor products of C(K) spaces according to whether none, exactly one or more than one factor contains copies of ℓ₁, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces or the verification of certain Banach space properties of the corresponding tensor product. The main tool is an improvement of some results of Emmanuele and Hensgen on the reciprocal Dunford-Pettis and Pełczyński's (V) properties of the projective...

Some classical function systems in separable Orlicz spaces

C. Finet, G. Tkebuchava (1996)

Studia Mathematica

The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.

Some common fixed point results for rational type contraction mappings in partially ordered metric spaces

Sumit Chandok (2013)

Mathematica Bohemica

The purpose of this paper is to establish some common fixed point results for f -nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).

Some common fixed point theorems in normed linear spaces

Alfred Olufemi Bosede (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we establish some generalizations to approximate common fixed points for selfmappings in a normed linear space using the modified Ishikawa iteration process with errors in the sense of Liu [10] and Rafiq [14]. We use a more general contractive condition than those of Rafiq [14] to establish our results. Our results, therefore, not only improve a multitude of common fixed point results in literature but also generalize some of the results of Berinde [3], Rhoades [15] and recent results...

Some commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1995)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the locally summable functions cos - ( λ x ) and cos + ( μ x ) is evaluated. Further similar commutative neutrix convolution products are evaluated and deduced.

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