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Daugavet centers and direct sums of Banach spaces

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Bosenko T.

Open Mathematics

2010

tom 8

nr 2

346-356

A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center acting into X 1⊕F X 2. We also present several examples of such Daugavet centers.

Ograniczanie wyników

1 Open Mathematics

1 Bosenko T.

1 2010

Wyniki wyszukiwania

Daugavet centers and direct sums of Banach spaces