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1996 | 121 | 1 | 1-14
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Köthe spaces modeled on spaces of $C^∞$ functions

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The isomorphic classification problem for the Köthe models of some $C^∞$ function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant $D_φ$ and other invariants related to the "quantity" characteristics of the space, a necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property $D_φ$ are not isomorphic.
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  • Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey
  • Rostov State University, Rostov-na-Donu, Russia
  • TÜBİTAK Marmara Research Center, 41470 Gebze, Kocaeli, Turkey
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  • [17] V. P. Zahariuta, Linear topological invariants and isomorphisms of spaces of analytic functions, Mat. Anal. i ego Prilozhen., Rostov Univ. 2 (1970), 3-13, 3 (1971), 176-180 (in Russian).
  • [18] V. P. Zahariuta, Generalized Mityagin invariants and a continuum of pairwise nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (3) (1977), 24-30 (in Russian).
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  • [21] V. P. Zahariuta, Linear topological invariants and their applications to isomorphic classification of generalized power spaces, Turkish J. Math. 20 (1996), 237-289.
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