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...
| Autores: | , , , , |
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| 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 |
| 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. |
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