Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis
Bellenot, Steven F.
Compositio Mathematica, Tome 42 (1980), p. 273-278 / Harvested from Numdam
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Publié le : 1980-01-01
@article{CM_1980__42_3_273_0,
     author = {Bellenot, Steven F.},
     title = {Each Schwartz Fr\'echet space is a subspace of a Schwartz Fr\'echet space with an unconditional basis},
     journal = {Compositio Mathematica},
     volume = {42},
     year = {1980},
     pages = {273-278},
     mrnumber = {607371},
     zbl = {0432.46003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1980__42_3_273_0}
}

Bellenot, Steven F. Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis. Compositio Mathematica, Tome 42 (1980) pp. 273-278. http://gdmltest.u-ga.fr/item/CM_1980__42_3_273_0/

[1] S.F. Bellenot: Prevarieties and intertwined completeness of locally convex spaces. Math. Ann. 217 (1975), 59-67. | MR 397347 | Zbl 0295.46013

[2] S.F. Bellenot: The Schwartz-Hilbert variety. Mich. Math. J. 22 (1975), 373-377. | MR 394086 | Zbl 0308.46002

[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. | MR 506670 | Zbl 0393.47015

[4] S.F. Bellenot: Basic sequences in non-Schwartz Fréchet spaces. Trans. Amer. Math. Soc. 258 (1980), 199-216. | MR 554329 | Zbl 0426.46001

[5] J. Diestel, S.A. Morris and S.A. Saxon: Varieties of linear topological spaces. Trans. Amer. Math. Soc. 172 (1972), 207-230. | MR 316992 | Zbl 0252.46001

[6] H. Jarchow: Die Universalität des Räumes c0 für die Klasse der Schwartz-Räume. Math. Ann. 203 (1973), 211-214. | MR 320700 | Zbl 0242.46032

[7] J.L. Kelly and T. Namioka: Linear Topological Spaces, Van Nostrand, 1963. | MR 166578 | Zbl 0115.09902

[8] G. Köthe: Topological Vector Spaces, I, Springer-Verlag, 1969. | MR 248498 | Zbl 0179.17001

[9] V.B. Moscatelli: Sur les espaces de Schwartz et ultranucléaires universels. C. R. Acad. Sc. Paris (serie A), 280 (1975), 937-940. | MR 383026 | Zbl 0312.46009

[10] A. Pietsch: Nuclear Locally Convex Spaces, Springer-Verlag, 1972. | MR 350360 | Zbl 0236.46001

[11] A. Pietsch: Ideals of operators on Banach spaces and locally convex spaces. Proc. III Symp. General Topology, Prague, 1971. | Zbl 0308.47024

[12] D.J. Randtke: A simple example of a universal Schwartz space. Proc. Amer. Math. Soc. 37 (1973), 185-188. | MR 312192 | Zbl 0251.46005

[13] D.J. Randtke: On the embedding of Schwartz spaces into product spaces. Proc. Amer. Math. Soc. 55 (1976), 87-92. | MR 410316 | Zbl 0343.46007