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

• Autorzy: Mefharet Kocatepe , Viacheslav P. Zahariuta
• 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.

Kategorie tematyczne

• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 46A45: Sequence spaces (including K\"othe sequence spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 121
• Numer: 1
• Strony: 1-14

Daty

wydano

1996

otrzymano

1995-04-26

poprawiono

1996-05-14

Twórcy

autor

Mefharet Kocatepe

• Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey

autor

Viacheslav P. Zahariuta

• Rostov State University, Rostov-na-Donu, Russia
• TÜBİTAK Marmara Research Center, 41470 Gebze, Kocaeli, Turkey

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.