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\(\Lambda_0\)-nuclear operators and \(\Lambda_0\)-nuclear spaces in \(p\)-adic analysis. (English) Zbl 0948.46052
Summary: For a Köthe sequence space, the classes of \(\Lambda_0\)-nuclear spaces and spaces with the \(\Lambda_0\)-property are introduced and studied and the relation between them is investigated. Also, we show that, for \(\Lambda_0\neq c_0\), these classes of spaces are in general different from the corresponding ones for \(\Lambda_0= c_0\), which have been extensively studied in the non-Archimedean literature.

MSC:
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A45 Sequence spaces (including Köthe sequence spaces)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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