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A problem on the structure of Fréchet spaces

Un problema sobre la estructura de espacios de Fréchet

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

The following open problem is stated: Is there a non-normable Fréchet space E such that every continuous linear operator T on E has the form T = λI + S, where S maps a 0-neighbourhood of E into a bounded set? A few remarks and the relation of this question with other still open problems on operators between Fréchet spaces are mentioned.

Resumen

Se plantea el siguiente problema: ≡Existe un espacio de Fréchet no normable E tal que todo operador lineal y continuo T en E tiene la forma T = λI + S, donde S manda un entorno de E en un conjunto acotado? Se mencionan algunas observaciones y la relación de esta cuestión con otros problemas aún abiertos acerca de operadores en espacios de Fréchet.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, E-46071, Valencia, Spain

    José Bonet

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  1. José Bonet
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Correspondence to José Bonet.

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Dedicated to Prof. Manuel Valdivia on the occasion of his 80th birthday

Submitted by Fernando Bombal

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Bonet, J. A problem on the structure of Fréchet spaces. RACSAM 104, 427–434 (2010). https://doi.org/10.5052/RACSAM.2010.26

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  • DOI: https://doi.org/10.5052/RACSAM.2010.26

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