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1999 | 137 | 1 | 33-47
Tytuł artykułu

Compound invariants and embeddings of Cartesian products

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
New compound geometric invariants are constructed in order to characterize complemented embeddings of Cartesian products of power series spaces. Bessaga's conjecture is proved for the same class of spaces.
Słowa kluczowe
Czasopismo
Rocznik
Tom
137
Numer
1
Strony
33-47
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-08-26
Twórcy
autor
  • Department of Mathematics, Rostov State University, Rostov-na-Donu, Russia
autor
  • Research Institute for Basic Sciences, TÜBİTAK, 41470 Gebze-Kocaeli, Turkey, zaha@mam.gov.tr
Bibliografia
  • [1] B C. Bessaga, Some remarks on Dragilev's theorem, Studia Math. 31 (1968), 307-318.
  • [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, A short proof of the theorem on quasi-equivalence of regular bases, Studia Math. 55 (1975), 269-271.
  • [4] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, On Cartesian products of Köthe spaces, Bull. Polish Acad. Sci. 43 (1996), 113-117.
  • [5] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, Isomorphic classification of Cartesian products of power series spaces, Michigan Math. J. 43 (1996), 221-229.
  • [6] M. M. Dragilev, On regular bases in nuclear spaces, Mat. Sb. 68 (1965), 153-173 (in Russian).
  • [7] M. M. Dragilev, Bases in Köthe Spaces, Rostov-na-Donu, 1983 (in Russian).
  • [8] A. N. Kolmogorov, On the linear dimension of topological vector spaces, Dokl. Akad. Nauk SSSR 120 (1958), 239-241 (in Russian).
  • [9] V. P. Kondakov, Problems of Geometry of Nonnormable Spaces, Rostov State University, Rostov-na-Donu, 1983 (in Russian).
  • [10] V. P. Kondakov, On structure of unconditional bases in some Köthe spaces, Studia Math. 76 (1983), 137-151 (in Russian).
  • [11] V. P. Kondakov and V. P. Zahariuta, On weak equivalence of bases in Köthe spaces, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Ser. Estestv. Nauk 4 (1982), 110-115 (in Russian).
  • [12] B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (1961), no. 4, 63-132 (in Russian).
  • [13] B. S. Mityagin, Sur l'équivalence des bases inconditionnelles dans les échelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428.
  • [14] B. S. Mityagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1970), 111-137 (in Russian).
  • [15] B. S. Mityagin, Non-Schwarzian power series spaces, Math. Z. 182 (1983), 303-310.
  • [16] A. Pełczyński, On the approximation of S-spaces by finite-dimensional spaces, Bull. Acad. Polon. Sci. 5 (1957), 879-881.
  • [17] M. Yurdakul and V. P. Zahariuta, Linear topological invariants and isomorphic classification of Cartesian products of locally convex spaces, Turkish J. Math. 19 (1995), 37-47.
  • [18] V. P. Zahariuta, On isomorphisms of Cartesian products of linear topological spaces, Funktsional. Anal. i Prilozhen. 4 (1970), no. 2, 87-88 (in Russian).
  • [19] V. P. Zahariuta, On the isomorphism of Cartesian products of locally convex spaces, Studia Math. 46 (1973), 201-221.
  • [20] V. P. Zahariuta, Linear topological invariants and isomorphisms of spaces of analytic functions, in: Matem. Analiz i ego Prilozhen. Rostov Univ., Vol. 2 (1970), 3-13, Vol. 3 (1971), 176-180 (in Russian).
  • [21] V. P. Zahariuta, Generalized Mityagin invariants and a continuum of pairwise nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (1977), no. 3, 24-30 (in Russian).
  • [22] V. P. Zahariuta, Synthetic diameters and linear topological invariants, in: School on the Theory of Operators in Function Spaces (abstracts of reports), Minsk, 1978, 51-52 (in Russian).
  • [23] V. P. Zahariuta, Linear Topological Invariants and Their Application to Generalized Power Spaces, Rostov Univ., 1979 (in Russian).
  • [24] V. P. Zahariuta, Linear topological invariants and their application to isomorphic classification of generalized power spaces, Turkish J. Math. 2 (1996), 237-289.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv137i1p33bwm
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