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In this paper we provide two representation theorems for two relevant classes of operators from any p-convex order continuous Banach lattice with weak unit into a Banach space: the class of continuous operators and the class of cone absolutely summing operators. We prove that they can be...

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The main aim of the paper is to prove a two-weight criterion for the multidimensional Hardy-type operator from weighted Lebesgue spaces into p-convex weighted Banach function spaces. The problem for the dual operator is also considered. As an application, we prove a two-weight criterion of...

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It is shown that for every 2-concave Banach lattice X of measurable fuctions on the circle, the quotient space X/XA has cotype 2. Here XA denotes the subclass of X consisting of the boundary values of analytic functions. It is also shown that, under slight additional assumptions, a p-concave...

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Let $$X(\mu )$$ be a p-convex ( $$1\le p<\infty $$) order continuous Banach function space over a positive finite measure $$\mu $$. We characterize the subspaces of $$X(\mu )$$ which can be found simultaneously in $$X(\mu )$$ and a suitable $$L^1(\eta )$$ space, where $$\eta $$ is a positive...

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We first introduce the concept of a p-convex metric space and a generalized p-quasicontractive mapping(or generalized quasicontractive mapping with respect to a weak distance p.) And also, we prove some convergence theorems of iterative sequences with errors for generalized p-quasicontractive...

- CONVERGENCE THEOREMS OF ITERATIVE SEQUENCES FOR GENERALIZED P-QUASICONTRACTIVE MAPPINGS IN P-CONVEX METRIC SPACES. Jong Kyu Kim; Sung-Ae Chun; Young Man Nam // Journal of Computational Analysis & Applications;Jan2008, Vol. 10 Issue 1, p147
We first introduce the concept of a p-convex metric space and a generalized p-quasicontractive mapping(or generalized quasicontractive mapping with respect to a weak distance p:) And also, we prove some convergence theorems of iterative sequences with errors for generalized p-quasicontractive...

- Interpolation of vector measures. Campo, Ricardo; Fernández, Antonio; Mayoral, Fernando; Naranjo, Francisco; Sánchez-Pérez, Enrique // Acta Mathematica Sinica;Jan2011, Vol. 27 Issue 1, p119
Let (Î©, Î£) be a measurable space and m: Î£ â†’ X and m: Î£ â†’ X be positive vector measures with values in the Banach KÃ¶the function spaces X and X. If 0 < Î± < 1, we define a new vector measure [ m, m] with values in the CalderÃ³n lattice interpolation space X X and...

- Strong extensions for q-summing operators acting in p-convex Banach function spaces for $$1 \le p \le q$$. Delgado, O.; Pérez, E. // Positivity;Dec2016, Vol. 20 Issue 4, p999
Let $$1\le p\le q<\infty $$ and let X be a p-convex Banach function space over a $$\sigma $$ -finite measure $$\mu $$ . We combine the structure of the spaces $$L^p(\mu )$$ and $$L^q(\xi )$$ for constructing the new space $$S_{X_p}^{\,q}(\xi )$$ , where $$\xi $$ is a probability Radon measure on...

- On Retro Banach Frames of Type P. Vashisht, L. K. // Azerbaijan Journal of Mathematics;Jan2012, Vol. 2 Issue 1, p87
Retro Banach frames of type P in Banach spaces have been introduced and studied. Necessary and sufficient conditions for existence of retro Banach frames of type P are obtained. A characterization of retro Banach frames obtained from translation of retro Banach frames of type P is given. Retro...

- Domination and factorization theorems for positive strongly $$p$$ -summing operators. Achour, D.; Belacel, A. // Positivity;Dec2014, Vol. 18 Issue 4, p785
The aim of this work is to contribute to the theory of $$(p,q)$$ -summing operators. We focus on positive $$(p,q)$$ -summing operators, introduced by Blasco (Collect Math 37(1):13-22, ). We characterize their conjugates and provide new domination/factorization theorems for these classes. As an...