On complemented subspaces of sums and products of Banach spaces
Author:
M. I. Ostrovskii
Journal:
Proc. Amer. Math. Soc. 124 (1996), 2005-2012
MSC (1991):
Primary 46A04, 46A13; Secondary 47B99
DOI:
https://doi.org/10.1090/S0002-9939-96-03413-2
MathSciNet review:
1328368
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that there exist complemented subspaces of countable topological products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces.
- [CK] P. G. Casazza and N. J. Kalton, Notes on approximation properties in separable Banach spaces, Geometry of Banach spaces (Strobl, 1989) London Math. Soc. Lecture Note Ser., vol. 158, Cambridge Univ. Press, Cambridge, 1990, pp. 49–63. MR 1110185
- [D1] Paweł Domański, Complemented subspaces of products of Hilbert spaces, Proc. Amer. Math. Soc. 110 (1990), no. 1, 187–196. MR 1000152, https://doi.org/10.1090/S0002-9939-1990-1000152-2
- [D2] Paweł Domański, ℒ_{𝓅}-spaces and injective locally convex spaces, Dissertationes Math. (Rozprawy Mat.) 298 (1990), 76. MR 1067609
- [DO] Paweł Domański and Augustyn Ortyński, Complemented subspaces of products of Banach spaces, Trans. Amer. Math. Soc. 316 (1989), no. 1, 215–231. MR 937243, https://doi.org/10.1090/S0002-9947-1989-0937243-4
- [J] William B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337–345. MR 290133, https://doi.org/10.1007/BF02771684
- [LT] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Springer-Verlag, Berlin-New York, 1977. Sequence spaces; Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. MR 0500056
- [MM1] G.Metafune and V.B.Moscatelli, Complemented subspaces of sums and products of Banach spaces, Ann. Mat. Pura Appl. 153 (1989), 1--16.
- [MM2] G. Metafune and V. B. Moscatelli, On twisted Fréchet and (LB)-spaces, Proc. Amer. Math. Soc. 108 (1990), no. 1, 145–150. MR 984806, https://doi.org/10.1090/S0002-9939-1990-0984806-X
- [MM3] G. Metafune and V. B. Moscatelli, Quojection and prequojections, Advances in the theory of Fréchet spaces (Istanbul, 1988) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 287, Kluwer Acad. Publ., Dordrecht, 1989, pp. 235–254. MR 1083567
- [R] C.J.Read, Different forms of the approximation property (to appear).
- [RR] A. P. Robertson and Wendy Robertson, Topological vector spaces, 2nd ed., Cambridge University Press, London-New York, 1973. Cambridge Tracts in Mathematics and Mathematical Physics, No. 53. MR 0350361
Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46A04, 46A13, 47B99
Retrieve articles in all journals with MSC (1991): 46A04, 46A13, 47B99
Additional Information
M. I. Ostrovskii
Affiliation:
Mathematical Division, Institute for Low Temperature Physics and Engineering, 47 Lenin avenue, 310164 Kharkov, Ukraine
Email:
mostrovskii@ilt.kharkov.ua
DOI:
https://doi.org/10.1090/S0002-9939-96-03413-2
Keywords:
Complemented subspace,
Banach space,
topological product of Banach spaces,
locally convex direct sum
Received by editor(s):
October 26, 1993
Received by editor(s) in revised form:
December 1, 1994
Communicated by:
Dale Alspach
Article copyright:
© Copyright 1996
American Mathematical Society