Interpolation of the inner measure of bilinear operators by the real method
We describe a procedure for extending the inner measure $\beta_{_{\mathcal{I}}}$ associated to an operator ideal $\mathcal{I}$ to a measure $\beta_{_{\mathfrak{J}}}$ for bounded bilinear operators $T$. When $\mathcal{I}$ is injective and close, we show that $\beta_{_{\mathfrak{J}}}(T)=0$ if and only...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/120646 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/120646 |
| Access Level: | acceso abierto |
| Palabra clave: | Inner measure of bilinear operators Real interpolation of bilinear operators Convexity inequalities Projective tensor products Ciencias 12 Matemáticas |
| Sumario: | We describe a procedure for extending the inner measure $\beta_{_{\mathcal{I}}}$ associated to an operator ideal $\mathcal{I}$ to a measure $\beta_{_{\mathfrak{J}}}$ for bounded bilinear operators $T$. When $\mathcal{I}$ is injective and close, we show that $\beta_{_{\mathfrak{J}}}(T)=0$ if and only if $T=RS$ for some bounded bilinear operator $S$ and $R\in\mathcal{I}$. If $\mathcal{I}$ satisfies the $\Sigma_r$-condition, then we establish a convexity inequality for the measure $\beta_{_{\mathfrak{J}}}$ of a bilinear operator interpolated by the real method. |
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