On Dragilev type power Köthe spaces

P. Djakov; V. Zahariuta

Studia Mathematica (1996)

  • Volume: 120, Issue: 3, page 219-234
  • ISSN: 0039-3223

Abstract

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A complete isomorphic classification is obtained for Köthe spaces X = K ( e x p [ χ ( p - κ ( i ) ) - 1 / p ] a i ) such that X q d ≃ 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.

How to cite

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Djakov, P., and Zahariuta, V.. "On Dragilev type power Köthe spaces." Studia Mathematica 120.3 (1996): 219-234. <http://eudml.org/doc/216333>.

@article{Djakov1996,
abstract = {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.},
author = {Djakov, P., Zahariuta, V.},
journal = {Studia Mathematica},
keywords = {isomorphic classification; Köthe spaces; quasi-equivalence property},
language = {eng},
number = {3},
pages = {219-234},
title = {On Dragilev type power Köthe spaces},
url = {http://eudml.org/doc/216333},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Djakov, P.
AU - Zahariuta, V.
TI - On Dragilev type power Köthe spaces
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 3
SP - 219
EP - 234
AB - 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.
LA - eng
KW - isomorphic classification; Köthe spaces; quasi-equivalence property
UR - http://eudml.org/doc/216333
ER -

References

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  1. [1] Dragilev M. M.: On special dimensions, defined on some classes of Köthe spaces, Mat. Sb. 80 (1969), 225-240 (in Russian). 
  2. [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. [3] Kondakov V. P.: Structure of unconditional bases of some Köthe spaces, Studia Math. 76 (1983), 137-151 (in Russian). Zbl0539.46010
  4. [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. [5] Mityagin B. S., Approximative dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (4) (1961), 63-132 (in Russian). 
  6. [6] Mityagin B. S., Sur l'équivalence des bases inconditionnelles dans les échelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428. Zbl0186.44704
  7. [7] Mityagin B. S., Equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137 (in Russian). 
  8. [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. [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. [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. [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. [12] Zahariuta, V. P., Linear topological invariants and their applications to generalized power series spaces, Turkish J. Math., to appear. Zbl0866.46005

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