On decompositions of Banach spaces into a sum of operator ranges

• Autorzy: V. P. Fonf , V. V. Shevchik
• 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 $l_1$.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 1
• Strony: 91-100

Daty

wydano

1999

otrzymano

1997-12-15

poprawiono

1998-03-27

Twórcy

autor

V. P. Fonf

• Department of Mathematics and Computer Sciences, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, Israel

autor

V. V. Shevchik

• Department of Mathematics and Informatics, Friedrich Schiller University, Lentragraben 1, 07743 Jena, Germany

Bibliografia

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