Quotients of Banach Spaces with the Daugavet Property

• Autorzy: Vladimir Kadets , Varvara Shepelska , Dirk Werner
• Języki publikacji: EN

Abstrakty

EN

We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak* analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of L₁[0,1] by an ℓ₁-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46B04: Isometric theory of Banach spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 2
• Strony: 131-147

Daty

wydano

2008

Twórcy

autor

Vladimir Kadets

• Department of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine

autor

Varvara Shepelska

• Department of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine

autor

Dirk Werner

• Department of Mathematics, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany

Identyfikatory

DOI

10.4064/ba56-2-5