Compound invariants and embeddings of Cartesian products

P. Chalov; P. Djakov; V. Zahariuta

Studia Mathematica (1999)

  • Volume: 137, Issue: 1, page 33-47
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Chalov, P., Djakov, P., and Zahariuta, V.. "Compound invariants and embeddings of Cartesian products." Studia Mathematica 137.1 (1999): 33-47. <http://eudml.org/doc/216673>.

@article{Chalov1999,
abstract = {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.},
author = {Chalov, P., Djakov, P., Zahariuta, V.},
journal = {Studia Mathematica},
keywords = {isomorphic classification; Köthe spaces; finite and infinite power series spaces; Bessaga's conjecture; compound invariants; embeddings of Cartesian products; Fréchet space; geometric invariants; power series spaces; complemented subspace},
language = {eng},
number = {1},
pages = {33-47},
title = {Compound invariants and embeddings of Cartesian products},
url = {http://eudml.org/doc/216673},
volume = {137},
year = {1999},
}

TY - JOUR
AU - Chalov, P.
AU - Djakov, P.
AU - Zahariuta, V.
TI - Compound invariants and embeddings of Cartesian products
JO - Studia Mathematica
PY - 1999
VL - 137
IS - 1
SP - 33
EP - 47
AB - 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.
LA - eng
KW - isomorphic classification; Köthe spaces; finite and infinite power series spaces; Bessaga's conjecture; compound invariants; embeddings of Cartesian products; Fréchet space; geometric invariants; power series spaces; complemented subspace
UR - http://eudml.org/doc/216673
ER -

References

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  2. [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. Zbl0109.33502
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  4. [4] P. B. Djakov, M. Yurdakul and V. P. Zahariuta, On Cartesian products of Köthe spaces, Bull. Polish Acad. Sci. 43 (1996), 113-117. Zbl0835.46004
  5. [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. Zbl0890.46008
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  9. [9] V. P. Kondakov, Problems of Geometry of Nonnormable Spaces, Rostov State University, Rostov-na-Donu, 1983 (in Russian). Zbl0614.46004
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  12. [12] B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (1961), no. 4, 63-132 (in Russian). Zbl0104.08601
  13. [13] B. S. Mityagin, Sur l'équivalence des bases inconditionnelles dans les échelles de Hilbert, C. R. Acad. Sci. Paris 269 (1969), 426-428. Zbl0186.44704
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  17. [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. Zbl0861.46005
  18. [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). 
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  20. [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. [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). 
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