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Alcuni risultati sugli insiemi prossiminali negli spazi di Banach

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Sommario

Scopo di questo lavoro è presentare alcuni recenti risultati sugli insiemi prossiminali negli spazi di Banach.

Speciale attenzione è dedicata al caso dello spazio delle funzioni reali continue: in particolare si introducono delle proprietà più forti della prossiminalità che consentono di dimostrare risultati nuovi anche nel caso della semplice prossiminalità.

Dato il carattere espositivo del lavoro, non sono in genere riportate le dimostrazioni dei teoremi.

Summary

Aim of this paper is to present some recent results on proximinal subsets of Banach spaces. The space of real continuous functions is especially considered: in particular some properties which are stronger than proximinality are introduced. By means of these properties some new results are proved also in the case of the usual proximinality.

Due to the expository character of this paper the proofs of the theorems are generally omitted.

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Referenze

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Authors and Affiliations

  1. dell’Università di Firenze, Firenze, Italia

    Carlo Franchetti

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  1. Carlo Franchetti
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(Conferenza tenuta il 24 ottobre 1983)

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Franchetti, C. Alcuni risultati sugli insiemi prossiminali negli spazi di Banach. Seminario Mat. e. Fis. di Milano 53, 49–63 (1983). https://doi.org/10.1007/BF02924883

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