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CN subspaces of nuclear spaces. (English. Russian original) Zbl 0958.46001

Sib. Math. J. 37, No. 3, 490-499 (1996); translation from Sib. Mat. Zh. 37, No. 3, 568-577 (1996).
Summary: Considered are the classes \(K\) of all nuclear Köthe spaces \(L_f(\lambda, \infty)\) and their isomorphic spaces as well as the class \(D^*\), a subclass of the spaces of generalized Dirichlet series \(A_\infty(F,\alpha)\) and their isomorphic copies. Since each infinite-dimensional countably normed nuclear space contains some subspace in \(K\) as well as in \(D^*\), the author asks to what extent \(K\) and \(D^*\) differ. He gives conditions under which GDS-spaces in \(D^*\) are isomorphic to a given space \(L_f(\lambda, \infty)\).

MSC:

46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A45 Sequence spaces (including Köthe sequence spaces)
46E10 Topological linear spaces of continuous, differentiable or analytic functions
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References:

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