Daugavet centers and direct sums of Banach spaces

• Autorzy: Tetiana Bosenko
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Daugavet center; Daugavet property; Direct sum of Banach spaces

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces
• 46B40: Ordered normed spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 2
• Strony: 346-356

Daty

wydano

2010-04-01

online

2010-04-14

Twórcy

autor

Tetiana Bosenko

• V.N. Karazin Kharkiv National University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0015-6