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L'Autore dà condizioni necessarie e sufficienti affinché uno spazio topologico sia omeomorfo al prodotto di un'infinito non-numerabile di rette.
Recentemente J. de Groot [3] ha dato una sufficiente caratterizzazione topologica assiomatica degli spazi [cubo metrico n dimensionale], [spazio euclideo n dimensionale], [cubo di Hilbert], [sfera n dimensionale] e [spazio proiettivo n dimensionale]. Lo scopo di questa Nota è di dare una caratterizzazione topologica assiomatica di [prodotto di un'infinità numerabile di rette reali] basata su una veduta e sul metodo di J. de Groot. Gli assiomi di J. de Groot per sono modificati per...
In this paper we discuss the problem of when the projective tensor product of two Banach spaces has the Radon-Nikodym property. We give a detailed exposition of the famous examples of Jean Bourgain and Gilles Pisier showing that there are Banach spaces X and Y such that each has the Radon-Nikodym property but for which their projective tensor product does not; this result depends on the classical theory of absolutely summing, integral and nuclear operators, as well as the famous Grothendieck inequality...
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