The Experts below are selected from a list of 30 Experts worldwide ranked by ideXlab platform
Enrique A. Sánchez-pérez - One of the best experts on this subject based on the ideXlab platform.
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Some inclusion results for interpolated summing operator ideals and integrability improvement of vector valued Functions
arXiv: Functional Analysis, 2016Co-Authors: Daniel Pellegrino, Pilar Rueda, Enrique A. Sánchez-pérezAbstract:Consider a Banach space valued measurable Function $f$ and an operator $u$ from the space where {$f$} takes values. If $f $ is Pettis Integrable, a classical result due to J. Diestel shows that composing it with $u$ gives a Bochner Integrable Function $u \circ f$ whenever $u$ is absolutely summing. In a previous work we have shown that a well-known interpolation technique for operator ideals allows to prove under some requirements that a composition of a $p$-Pettis Integrable Function with a $q$-summing operator provides an $r$-Bochner Integrable Function. In this paper a new abstract inclusion theorem for classes of {abstract} summing operators is shown and applied to the class of interpolated operator ideals. Together with the results of the {aforementioned} paper, it provides more results on the relation about the integrability of the Function $u \circ f$ and the summability properties of $u$.
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Improving integrability via absolute summability: a general version of Diestel's Theorem
Positivity, 2015Co-Authors: Daniel Pellegrino, Pilar Rueda, Enrique A. Sánchez-pérezAbstract:A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis Integrable Function gives a Bochner Integrable Function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued Functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the \((p,\sigma )\)-absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces—including C(K), \(L^p\) and Hilbert spaces—and operators—p-summing, (q, p)-summing and p-approximable operators.
Daniel Pellegrino - One of the best experts on this subject based on the ideXlab platform.
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Some inclusion results for interpolated summing operator ideals and integrability improvement of vector valued Functions
arXiv: Functional Analysis, 2016Co-Authors: Daniel Pellegrino, Pilar Rueda, Enrique A. Sánchez-pérezAbstract:Consider a Banach space valued measurable Function $f$ and an operator $u$ from the space where {$f$} takes values. If $f $ is Pettis Integrable, a classical result due to J. Diestel shows that composing it with $u$ gives a Bochner Integrable Function $u \circ f$ whenever $u$ is absolutely summing. In a previous work we have shown that a well-known interpolation technique for operator ideals allows to prove under some requirements that a composition of a $p$-Pettis Integrable Function with a $q$-summing operator provides an $r$-Bochner Integrable Function. In this paper a new abstract inclusion theorem for classes of {abstract} summing operators is shown and applied to the class of interpolated operator ideals. Together with the results of the {aforementioned} paper, it provides more results on the relation about the integrability of the Function $u \circ f$ and the summability properties of $u$.
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Improving integrability via absolute summability: a general version of Diestel's Theorem
Positivity, 2015Co-Authors: Daniel Pellegrino, Pilar Rueda, Enrique A. Sánchez-pérezAbstract:A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis Integrable Function gives a Bochner Integrable Function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued Functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the \((p,\sigma )\)-absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces—including C(K), \(L^p\) and Hilbert spaces—and operators—p-summing, (q, p)-summing and p-approximable operators.
E. A. Sánchez-pérez - One of the best experts on this subject based on the ideXlab platform.
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Improving integrability via absolute summability: a general version of Diestel’s Theorem
Positivity, 2016Co-Authors: D. Pellegrino, P. Rueda, E. A. Sánchez-pérezAbstract:A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis Integrable Function gives a Bochner Integrable Function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued Functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the $$(p,\sigma )$$ ( p , σ ) -absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces—including C ( K ), $$L^p$$ L p and Hilbert spaces—and operators— p -summing, ( q , p )-summing and p -approximable operators.
Pilar Rueda - One of the best experts on this subject based on the ideXlab platform.
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Some inclusion results for interpolated summing operator ideals and integrability improvement of vector valued Functions
arXiv: Functional Analysis, 2016Co-Authors: Daniel Pellegrino, Pilar Rueda, Enrique A. Sánchez-pérezAbstract:Consider a Banach space valued measurable Function $f$ and an operator $u$ from the space where {$f$} takes values. If $f $ is Pettis Integrable, a classical result due to J. Diestel shows that composing it with $u$ gives a Bochner Integrable Function $u \circ f$ whenever $u$ is absolutely summing. In a previous work we have shown that a well-known interpolation technique for operator ideals allows to prove under some requirements that a composition of a $p$-Pettis Integrable Function with a $q$-summing operator provides an $r$-Bochner Integrable Function. In this paper a new abstract inclusion theorem for classes of {abstract} summing operators is shown and applied to the class of interpolated operator ideals. Together with the results of the {aforementioned} paper, it provides more results on the relation about the integrability of the Function $u \circ f$ and the summability properties of $u$.
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Improving integrability via absolute summability: a general version of Diestel's Theorem
Positivity, 2015Co-Authors: Daniel Pellegrino, Pilar Rueda, Enrique A. Sánchez-pérezAbstract:A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis Integrable Function gives a Bochner Integrable Function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued Functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the \((p,\sigma )\)-absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces—including C(K), \(L^p\) and Hilbert spaces—and operators—p-summing, (q, p)-summing and p-approximable operators.
D. Pellegrino - One of the best experts on this subject based on the ideXlab platform.
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Improving integrability via absolute summability: a general version of Diestel’s Theorem
Positivity, 2016Co-Authors: D. Pellegrino, P. Rueda, E. A. Sánchez-pérezAbstract:A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis Integrable Function gives a Bochner Integrable Function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued Functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the $$(p,\sigma )$$ ( p , σ ) -absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces—including C ( K ), $$L^p$$ L p and Hilbert spaces—and operators— p -summing, ( q , p )-summing and p -approximable operators.