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1996 | 121 | 1 | 1-14
Tytuł artykułu

Köthe spaces modeled on spaces of $C^∞$ functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
121
Numer
1
Strony
1-14
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-04-26
poprawiono
1996-05-14
Twórcy
Bibliografia
  • [1] H. Apiola, Characterization of subspaces and quotients of nuclear $L_f(α,∞)$-spaces, Compositio Math. 50 (1983), 65-81.
  • [2] C. Bessaga, A. Pełczyński and S. Rolewicz, On diametral approximative dimension and linear homogeneity of F-spaces, Bull. Acad. Polon. Sci. 9 (1961), 677-683.
  • [3] P. B. Djakov and V. P. Zahariuta, On Dragilev type power spaces, preprint.
  • [4] I. M. Gelfand, On some problems of functional analysis, Uspekhi Mat. Nauk 11 (6) (1956), 3-12 (in Russian).
  • [5] A. P. Goncharov, Isomorphic classifications of spaces of infinitely differentiable functions, dissertation, Rostov University, 1986 (in Russian).
  • [6] A. P. Goncharov and V. P. Zahariuta, Linear topological invariants and spaces of infinitely differentiable functions, Mat. Anal. i ego Prilozhen., Rostov State University, 1985, 18-27 (in Russian).
  • [7] A. P. Goncharov and V. P. Zahariuta, On the existence of bases in spaces of Whitney functions on special compact sets in ℝ, preprint.
  • [8] A. N. Kolmogorov, On the linear dimension of topological vector spaces, Dokl. Akad. Nauk SSSR 120 (1958), 239-341 (in Russian).
  • [9] V. P. Kondakov and V. P. Zahariuta, On bases in spaces of infinitely differentiable functions on special domains with cusp, Note Mat. 12 (1992), 99-106.
  • [10] B. S. Mityagin, Approximate dimension and bases in nuclear spaces, Russian Math. Surveys 16 (4) (1961), 59-127.
  • [11] B. S. Mityagin, Sur l'équivalence des bases inconditionnelles dans les échelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428.
  • [12] B. S. Mityagin, The equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137 (in Russian).
  • [13] B. S. Mityagin, Non-Schwartzian power series spaces, Math. Z. 182 (1983), 303-310.
  • [14] A. Pełczyński, On the approximation of S-spaces by finite-dimensional spaces, Bull. Acad. Polon. Sci. 5 (1957), 879-881.
  • [15] M. Tidten, An example of a continuum of pairwise non-isomorphic spaces of $C^∞$ functions, Studia Math. 78 (1984), 267-274.
  • [16] D. Vogt, Some results on continuous linear maps between Fréchet spaces, in: Functional Analysis: Surveys and Recent Results III, K. D. Bierstedt and B. Fuchssteiner (eds.), North-Holland Math. Stud. 90, North-Holland, 1984, 349-381.
  • [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).
  • [19] V. P. Zahariuta, Synthetic diameters and linear topological invariants, in: School on Theory of Operators in Functional Spaces (abstracts of reports), Minsk, 1978, 51-52 (in Russian).
  • [20] V. P. Zahariuta, On isomorphic classification of F-spaces, in: Linear and Complex Analysis Problem Book, 199 Research Problems, Lecture Notes in Math. 1043, Springer, 1984, 34-37.
  • [21] V. P. Zahariuta, Linear topological invariants and their applications to isomorphic classification of generalized power spaces, Turkish J. Math. 20 (1996), 237-289.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv121i1p1bwm
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