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## Studia Mathematica

1999 | 132 | 1 | 91-100
Tytuł artykułu

### On decompositions of Banach spaces into a sum of operator ranges

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is proved that a separable Banach space X admits a representation $X = X_1 + X_2$ as a sum (not necessarily direct) of two infinite-codimensional closed subspaces $X_1$ and $X_2$ if and only if it admits a representation $X = A_1(Y_1) + A_2(Y_2)$ as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation $X = T_1(Z_1) + T_2(Z_2)$ such that neither of the operator ranges $T_1(Z_1)$, $T_2(Z_2)$ contains an infinite-dimensional closed subspace if and only if X does not contain an isomorphic copy of $l_1$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
91-100
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-12-15
poprawiono
1998-03-27
Twórcy
autor
• Department of Mathematics and Computer Sciences, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel, fonf@black.bgu.ac.il
autor
• Department of Mathematics and Informatics, Friedrich Schiller University, Lentragraben 1, 07743 Jena, Germany, shevchik@minet.uni-jena.
Bibliografia
• [1] Fillmore P. A., and Williams J. P., On operator ranges, Adv. Math. 7 (1971), 254-281.
• [2] Fonf V. P., On supportless absorbing convex subsets in normed spaces, Studia Math. 104 (1993), 279-284.
• [3] Fonf V. P., and Shevchik V. V., Representing a Banach space as a sum of operator ranges, Funct. Anal. Appl. 29 (1995), no. 3, 220-221 (transl. from the Russian).
• [4] Gowers W. T., and Maurey B., The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
• [5] Johnson W. B., and Rosenthal H. P., On w*-basic sequences and their applications to the study of Banach spaces, Studia Math. 43 (1972), 77-92.
• [6] Lindenstrauss J., and Tzafriri L., Classical Banach Spaces, Vol. 1, Springer, Berlin, 1977.
• [7] Pełczyński A., On strictly singular and strictly cosingular operators, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys. 13 (1965), 31-41.
• [8] Pietsch A., Operator Ideals, North-Holland, Amsterdam, 1980.
Typ dokumentu
Bibliografia
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