Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis

Steven F. Bellenot

Compositio Mathematica (1980)

  • Volume: 42, Issue: 3, page 273-278
  • ISSN: 0010-437X

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Bellenot, Steven F.. "Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis." Compositio Mathematica 42.3 (1980): 273-278. <http://eudml.org/doc/89479>.

@article{Bellenot1980,
author = {Bellenot, Steven F.},
journal = {Compositio Mathematica},
keywords = {Schwartz variety; barreled; bornological; Schwartz space; Frechet space; Köthe sequence space; unconditional basis; universal generator},
language = {eng},
number = {3},
pages = {273-278},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis},
url = {http://eudml.org/doc/89479},
volume = {42},
year = {1980},
}

TY - JOUR
AU - Bellenot, Steven F.
TI - Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 42
IS - 3
SP - 273
EP - 278
LA - eng
KW - Schwartz variety; barreled; bornological; Schwartz space; Frechet space; Köthe sequence space; unconditional basis; universal generator
UR - http://eudml.org/doc/89479
ER -

References

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  1. [1] S.F. Bellenot: Prevarieties and intertwined completeness of locally convex spaces. Math. Ann.217 (1975), 59-67. Zbl0295.46013MR397347
  2. [2] S.F. Bellenot: The Schwartz-Hilbert variety. Mich. Math. J.22 (1975), 373-377. Zbl0308.46002MR394086
  3. [3] S.F. Bellenot: Factorization of compact operators and uniform finite representability of Banach spaces with applications to Schwartz spaces. Studia Math.62 (1978) 273-286. Zbl0393.47015MR506670
  4. [4] S.F. Bellenot: Basic sequences in non-Schwartz Fréchet spaces. Trans. Amer. Math. Soc.258 (1980), 199-216. Zbl0426.46001MR554329
  5. [5] J. Diestel, S.A. Morris and S.A. Saxon: Varieties of linear topological spaces. Trans. Amer. Math. Soc.172 (1972), 207-230. Zbl0252.46001MR316992
  6. [6] H. Jarchow: Die Universalität des Räumes c0 für die Klasse der Schwartz-Räume. Math. Ann.203 (1973), 211-214. Zbl0242.46032MR320700
  7. [7] J.L. Kelly and T. Namioka: Linear Topological Spaces, Van Nostrand, 1963. Zbl0115.09902MR166578
  8. [8] G. Köthe: Topological Vector Spaces, I, Springer-Verlag, 1969. Zbl0179.17001MR248498
  9. [9] V.B. Moscatelli: Sur les espaces de Schwartz et ultranucléaires universels. C. R. Acad. Sc. Paris (serie A), 280 (1975), 937-940. Zbl0312.46009MR383026
  10. [10] A. Pietsch: Nuclear Locally Convex Spaces, Springer-Verlag, 1972. Zbl0236.46001MR350360
  11. [11] A. Pietsch: Ideals of operators on Banach spaces and locally convex spaces. Proc. III Symp. General Topology, Prague, 1971. Zbl0308.47024
  12. [12] D.J. Randtke: A simple example of a universal Schwartz space. Proc. Amer. Math. Soc.37 (1973), 185-188. Zbl0251.46005MR312192
  13. [13] D.J. Randtke: On the embedding of Schwartz spaces into product spaces. Proc. Amer. Math. Soc.55 (1976), 87-92. Zbl0343.46007MR410316

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