On Dragilev type power Köthe spaces

• Autorzy: P. B. Djakov , V. P. Zahariuta
• Języki publikacji: EN

Abstrakty

EN

A complete isomorphic classification is obtained for Köthe spaces $X = K(exp[χ(p - κ (i)) - 1/p]a_i)$ such that $X qd_≃ X^2$; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and $a_i → ∞$. Any of these spaces has the quasi-equivalence property.

Słowa kluczowe

EN

isomorphic classification; Köthe spaces

Kategorie tematyczne

• 46A45: Sequence spaces (including K\"othe sequence spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 120
• Numer: 3
• Strony: 219-234

Daty

wydano

1996

otrzymano

1995-03-10

poprawiono

1996-04-12

Twórcy

autor

P. B. Djakov

• Department of Mathematics, Sofia University, 1164 Sofia, Bulgaria,

autor

V. P. Zahariuta

• Department of Mechanics and Mathematics, Rostov State University, Rostov-na-Donu, Russia,
• Department of Mathematics, Marmara Research Center, Gebze, Kocaeli, Turkey

Bibliografia

• [1] Dragilev M. M.: On special dimensions, defined on some classes of Köthe spaces, Mat. Sb. 80 (1969), 225-240 (in Russian).
• [2] Hall M.: A survey of combinatorial analysis, in: Some Aspects of Analysis and Probability, Surveys Appl. Math. 4, Wiley, New York, 1958, 35-104.
• [3] Kondakov V. P.: Structure of unconditional bases of some Köthe spaces, Studia Math. 76 (1983), 137-151 (in Russian).
• [4] V. P. Kondakov and V. P. Zahariuta, On weak equivalence of bases in Köthe spaces, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk 4 (1982), 110-115 (in Russian).
• [5] Mityagin B. S., Approximative dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (4) (1961), 63-132 (in Russian).
• [6] Mityagin B. S., Sur l'équivalence des bases inconditionnelles dans les échelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428.
• [7] Mityagin B. S., Equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137 (in Russian).
• [8] Zahariuta, V. P., On isomorphisms of Cartesian products of linear topological spaces, Funktsional. Anal. i Prilozhen. 4 (2) (1970), 87-88 (in Russian).
• [9] Zahariuta, V. P., On isomorphisms and quasi-equivalence of bases of power Köthe spaces, in: Proc. 7th Winter School in Drogobych, Moscow, 1976, 101-126 (in Russian).
• [10] Zahariuta, V. P., Generalized Mityagin invariants and a continuum of pairwise nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (3) (1977), 24-30 (in Russian).
• [11] Zahariuta, V. P., Synthetic diameters and linear topological invariants, in: School on Theory of Operators in Function Spaces (abstracts of reports), Minsk, 1978, 51-52 (in Russian).
• [12] Zahariuta, V. P., Linear topological invariants and their applications to generalized power series spaces, Turkish J. Math., to appear.