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On Grothendieck space ideals. (English) Zbl 0718.46002
Summary: We develop some techniques to prove that some well known classes of Schwartz spaces cannot be generated by a pre-ideal of operators. We also construct new proofs for Montel spaces and spaces of maximal diametral dimension.

MSC:
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
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