Artículo
Optimal Extensions for pth Power Factorable Operators
Autor/es | Delgado Garrido, Olvido
Sánchez Pérez, E. A. |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2016 |
Fecha de depósito | 2021-01-11 |
Publicado en |
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Resumen | Let X(μ) be a function space related to a measure space
(Ω,Σ, μ) with χΩ ∈ X(μ) and let T : X(μ) → E be a Banach spacevalued
operator. It is known that if T is pth power factorable then the
largest function space to ... Let X(μ) be a function space related to a measure space (Ω,Σ, μ) with χΩ ∈ X(μ) and let T : X(μ) → E be a Banach spacevalued operator. It is known that if T is pth power factorable then the largest function space to which T can be extended preserving pth power factorability is given by the space Lp(mT) of p-integrable functions with respect to mT, where mT : Σ → E is the vector measure associated to T via mT (A) = T(χA). In this paper, we extend this result by removing the restriction χΩ ∈ X(μ). In this general case, by considering mT defined on a certain δ-ring, we show that the optimal domain for T is the space Lp(mT )∩L1(mT ). We apply the obtained results to the particular case when T is a map between sequence spaces defined by an infinite matrix. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España Junta de Andalucía |
Identificador del proyecto | MTM2012-36732-C03-03
FQM-262 FQM-7276 |
Cita | Delgado Garrido, O. y Sánchez Pérez, E.A. (2016). Optimal Extensions for pth Power Factorable Operators. Mediterranean Journal of Mathematics, 13 (6), 4281-4303. |
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