On the embedding of Schwartz spaces into product spaces
Author:
Daniel J. Randtke
Journal:
Proc. Amer. Math. Soc. 55 (1976), 87-92
MSC:
Primary 46A15
DOI:
https://doi.org/10.1090/S0002-9939-1976-0410316-7
MathSciNet review:
0410316
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Every Schwartz space is embeddable into some sufficiently high power of a given Banach space
if and only if
contains
uniformly.
- [1] S. F. Bellenot, Factorable bounded operators and Schwartz spaces, Proc. Amer. Math. Soc. 42 (1974), 551-554. MR 48 #6899. MR 0328557 (48:6899)
- [2] J. Diestel and R. H. Lohman, Applications of mapping theorems to Schwartz spaces and projections, Michigan Math. J. 20 (1973), 39-44. MR 47 #5541. MR 0316993 (47:5541)
- [3] T. Figiel, Factorization of compact operators and applications to the approximation problem, Studia Math. 45 (1973), 191-210. MR 0336294 (49:1070)
- [4] D. J. H. Garling and Y. Gordon, Relations between some constants associated with finite dimensional Banach spaces, Israel J. Math. 9 (1971), 346-361. MR 0412775 (54:896)
- [5] J. M. Horváth, Topological vector spaces and distributions, Vol. I, Addison-Wesley, Reading, Mass., 1966. MR 34 #4863. MR 0205028 (34:4863)
- [6]
H. Jarchow, Die Universalität des Raumes
für die Klasse der Schwartz-Räume, Math. Ann. 203 (1973), 211-214. MR 47 #9235. MR 0320700 (47:9235)
- [7]
J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in
-spaces and their applications, Studia Math. 29 (1968), 275-326. MR 37 #6743. MR 0231188 (37:6743)
- [8]
J. Lindenstrauss and H. P. Rosenthal, The
spaces, Israel J. Math. 7 (1969), 325-349. MR 42 #5012. MR 0270119 (42:5012)
- [9] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Springer-Verlag, Berlin and New York, 1973. MR 0415253 (54:3344)
- [10]
B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces
, Asterisque, 11, Société Mathématique de France, 1974. MR 0344931 (49:9670)
- [11] D. J. Randtke, A structure theorem for Schwartz spaces, Math. Ann. 201 (1973), 171-176. MR 48 #4691. MR 0326347 (48:4691)
- [12] -, A simple example of a universal Schwartz space, Proc. Amer. Math. Soc. 37 (1973), 185-188. MR 47 #754. MR 0312192 (47:754)
- [13] S. A. Saxon, Embedding nuclear spaces in products of an arbitrary Banach space, Proc. Amer. Math. Soc. 34 (1972), 138-140. MR 47 #7369. MR 0318823 (47:7369)
- [14] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1689. MR 0193469 (33:1689)
- [15] T. Terzioğlu, A characterization of compact linear mappings, Arch. Math. 22 (1971), 76-78. MR 0291865 (45:954)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A15
Retrieve articles in all journals with MSC: 46A15
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1976-0410316-7
Keywords:
Compact linear operator,
subspace factorization property,
contains uniformly,
universal Schwartz space,
Schwartz space
Article copyright:
© Copyright 1976
American Mathematical Society