Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis

Jörg Krone; Volker Walldorf

Studia Mathematica (1998)

  • Volume: 127, Issue: 1, page 1-7
  • ISSN: 0039-3223

Abstract

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The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.

How to cite

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Krone, Jörg, and Walldorf, Volker. "Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis." Studia Mathematica 127.1 (1998): 1-7. <http://eudml.org/doc/216457>.

@article{Krone1998,
abstract = {The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.},
author = {Krone, Jörg, Walldorf, Volker},
journal = {Studia Mathematica},
keywords = {nuclear Köthe spaces; basis; finite-dimensional decomposition; complemented subspaces; Köthe matrix; Fréchet space; Grothendieck-Pietsch criterion},
language = {eng},
number = {1},
pages = {1-7},
title = {Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis},
url = {http://eudml.org/doc/216457},
volume = {127},
year = {1998},
}

TY - JOUR
AU - Krone, Jörg
AU - Walldorf, Volker
TI - Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis
JO - Studia Mathematica
PY - 1998
VL - 127
IS - 1
SP - 1
EP - 7
AB - The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.
LA - eng
KW - nuclear Köthe spaces; basis; finite-dimensional decomposition; complemented subspaces; Köthe matrix; Fréchet space; Grothendieck-Pietsch criterion
UR - http://eudml.org/doc/216457
ER -

References

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  1. [1] C. Bessaga, Some remarks on Dragilev's theorem, Studia Math. 31 (1968), 307-318. Zbl0182.45301
  2. [2] P. B. Djakov and E. Dubinsky, Complemented block subspaces of Köthe spaces, Serdica 14 (1988), 278-282. 
  3. [3] P. B. Djakov and B. S. Mityagin, Modified construction of a nuclear Fréchet space without basis, J. Funct. Anal. 23 (1976), 415-423. 
  4. [4] E. Dubinsky, Subspaces without basis in nuclear Fréchet spaces, J. Funct. Anal. 26 (1977), 121-130. Zbl0444.46005
  5. [5] E. Dubinsky, The Structure of Nuclear Fréchet Spaces, Lecture Notes in Math. 720, Springer, Berlin, 1979. Zbl0403.46005
  6. [6] E. Dubinsky and B. S. Mityagin, Quotient spaces without basis in nuclear Fréchet spaces, Canad. J. Math. 30 (1978), 1296-1305. Zbl0399.46003
  7. [7] G. Köthe, Topologische lineare Räume, Springer, 1960. Zbl0093.11901
  8. [8] J. Krone, On Pełczyński's problem, in: Advances in the Theory of Fréchet Spaces, T. Terzioğlu (ed.), NATO Adv. Sci. Inst. Ser. C 287, Kluwer Acad. Publ., 1989, 297-304. Zbl0804.46005
  9. [9] R. Meise und D. Vogt, Einführung in die Funktionalanalysis, Vieweg, 1992. 
  10. [10] A. Pełczyński, Problem 37, Studia Math. 38 (1970), 476. 
  11. [11] A. Pietsch, Nuclear Locally Convex Spaces, Ergeb. Math. 66, Springer, 1972. 
  12. [12] M. J. Wagner, Some new methods in the structure theory of nuclear Fréchet spaces, in: Advances in the Theory of Fréchet spaces, T. Terzioğlu (ed.), NATO Adv. Sci. Inst. Ser. C 287, Kluwer Acad. Publ., 1989, 333-354. 

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