Diametral dimensions of Cartesian products, stability of smooth sequence spaces and applications.

The purpose of this paper is to demonstrate considerable similarities in the behaviour of compact and O)-nuclear operators. More precisely, we obtain for (s)-nuclear operators results resembling previously known properties of compact operators; sometimes a word for word translation of a "compact theorem" holds for (s)-nudear operators. However, we wish to emphasize that different methods for the proofs are now needed. For example, the often applied Ascoli-Arzela theorem does not have a (s)-nuclear counterpart (see §5).

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On the equality between two diametral dimensions

Bastin¹,

Demeulenaere²

2017

Funct. Approx. Comment. Math.

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Diametral dimensions of Cartesian products, stability of smooth sequence spaces and applications.

Cited by 3 publications

References 5 publications

λ-Bases and their applications

λ-Bases and their applications

(s)-nuclear sets and operators

On the equality between two diametral dimensions

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