Complex Interpolation of Operators and Optimal Domains

Let X0 and X1 be two order continuous Banach function spaces on a finite measure space, (E0, E1) a Banach space interpolation pair, and T : X0 + X1 → E0 + E1 an admissible operator between the pairs (X0, X1) and (E0, E1). If Tθ : [X0, X1][θ] → [E0, E1][θ] is the inter polated operator by the first c...

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Detalhes bibliográficos
Autores: Campo Acosta, Ricardo del, Fernández Carrión, Antonio, Galdames, Orlando, Mayoral Masa, Fernando, Naranjo Naranjo, Francisco José
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2014
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/135882
Acesso em linha:https://hdl.handle.net/11441/135882
https://doi.org/10.1007/s00020-014-2158-5
Access Level:Acceso aberto
Palavra-chave:Banach function space
Optimal domain
Interpolation space
Vector measures
Factorable operator
Bidual concave operator
Descrição
Resumo:Let X0 and X1 be two order continuous Banach function spaces on a finite measure space, (E0, E1) a Banach space interpolation pair, and T : X0 + X1 → E0 + E1 an admissible operator between the pairs (X0, X1) and (E0, E1). If Tθ : [X0, X1][θ] → [E0, E1][θ] is the inter polated operator by the first complex method of Calder´on and m0, m1 and mθ are the vector measures coming from T| X0 and T| X1 and Tθ, respectively, then we study the relationship between the optimal domain L1(mθ) of Tθ and the complex interpolation space [L1(m0), L1(m1)][θ] of the optimal domains of T| X0 and T| X1 . Then, we apply the obtained result to study interpolation of p-th power factorable and bidual (p, q)- power-concave operators.