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On supportless absorbing convex subsets in normed spaces

100%

Fonf V. P.

Studia Mathematica

1993

tom 104

nr 3

279-284

It is proved that a separable normed space contains a closed bounded convex symmetric absorbing supportless subset if and only if this space may be covered (in its completion) by the range of a nonisomorphic operator.

On decompositions of Banach spaces into a sum of operator ranges

63%

Fonf V. P., Shevchik V.

Studia Mathematica

1999

tom 132

nr 1

91-100

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 $l_1$.

Ograniczanie wyników

2 Studia Mathematica

2 Fonf V. P.

1 Shevchik V.

1 1999

1 1993

Wyniki wyszukiwania

On supportless absorbing convex subsets in normed spaces

On decompositions of Banach spaces into a sum of operator ranges