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On complemented subspaces of sums and products of Banach spaces
Author(s):
M.
I.
Ostrovskii
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2005-2012.
MSC (1991):
Primary 46A04, 46A13;
Secondary 47B99
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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.
References:
- [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., 158 (P.Müller and W.Schachermayer, eds.), Cambridge University Press, 1990, pp. 49--63. MR 92d:46022
- [D1]
- P.Domanski, Complemented subspaces of products of Hilbert spaces, Proc. Amer. Math. Soc. 110 (1990), 187--196. MR 90m:46007
- [D2]
- ------,
 -spaces and injective locally convex spaces, Rozprawy Mat. 298 (1990), 1--76. MR 91j:46002 - [DO]
- P.Doma\'{n}ski and A.Orty\'{n}ski, Complemented subspaces of products of Banach spaces, Trans. Amer. Math. Soc. 316 (1989), 215--231. MR 90b:46004
- [J]
- W.B.Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337--345. MR 44:7318
- [LT]
- J.Lindenstrauss and L.Tzafriri, Classical Banach spaces, v. I, Springer--Verlag, Berlin Heidelberg New York, 1977. MR 58:17766
- [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]
- ------, On twisted Fréchet and (LB)-spaces, Proc. Amer. Math. Soc. 108 (1990), 145--150. MR 90d:46007
- [MM3]
- ------, Quojections and prequojections, Advances in the Theory of Fréchet spaces (T.Terzioglu, ed.), Kluwer Academic Publishers, Dordrecht, 1989, pp. 235--254. MR 92e:46006
- [R]
- C.J.Read, Different forms of the approximation property (to appear).
- [RR]
- A.P.Robertson and W.Robertson, Topological vector spaces, Cambridge University Press, Cambridge, 1973. MR 50:2854
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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:
10.1090/S0002-9939-96-03413-2
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Albanese, A.A.; Moscatelli, V.B., Complemented subspaces of sums and products of copies of $L\sp 1[0,1]$,Rev. Mat. Univ. Complutense Madrid 9(1996), 275-287. (English)
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