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Geometric aspects of the Daugavet property
 J. Funct. Anal
, 2000
"... Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X,Y) has the Daugavet property if for every rank one bounded linear operator T from X to Y the following equality ‖J + T ‖ = 1 + ‖T ‖ (1) holds. A new characterization of the Daugavet property in terms ..."
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Cited by 20 (3 self)
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Let X be a closed subspace of a Banach space Y and J be the inclusion map. We say that the pair (X,Y) has the Daugavet property if for every rank one bounded linear operator T from X to Y the following equality ‖J + T ‖ = 1 + ‖T ‖ (1) holds. A new characterization of the Daugavet property in terms
Banach spaces with the Daugavet property
 Trans. Amer. Math. Soc
"... Abstract. A Banach space X is said to have the Daugavet property if every operator T: X → X of rank 1 satisfies ‖Id+T ‖ = 1+‖T ‖. We show that then every weakly compact operator satisfies this equation as well and that X contains a copy of ℓ1. However, X need not contain a copy of L1. We also study ..."
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Cited by 48 (24 self)
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Abstract. A Banach space X is said to have the Daugavet property if every operator T: X → X of rank 1 satisfies ‖Id+T ‖ = 1+‖T ‖. We show that then every weakly compact operator satisfies this equation as well and that X contains a copy of ℓ1. However, X need not contain a copy of L1. We also
Recent Progress on the Daugavet Property
 IRISH MATH. SOC. BULLETIN 46 (2001), 77–97
, 2001
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The Daugavet property for spaces of Lipschitz functions
, 2005
"... Abstract. For a compact metric space K the space Lip(K) has the Daugavet property if and only if the norm of every f ∈ Lip(K) is attained locally. If K is a subset of an Lpspace, 1 < p < ∞, this is equivalent to the convexity of K. 1. ..."
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Cited by 6 (3 self)
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Abstract. For a compact metric space K the space Lip(K) has the Daugavet property if and only if the norm of every f ∈ Lip(K) is attained locally. If K is a subset of an Lpspace, 1 < p < ∞, this is equivalent to the convexity of K. 1.
The Daugavet Property of the Space of Lipschitz Functions
"... Abstract. In this paper we will prove that the Banach space of Lipschitz functions on a compact convex set in a Banach space and the Banach space of continuously differentiable functions on a closure of some bounded domain in R n possess the Daugavet property. ..."
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Abstract. In this paper we will prove that the Banach space of Lipschitz functions on a compact convex set in a Banach space and the Banach space of continuously differentiable functions on a closure of some bounded domain in R n possess the Daugavet property.
Narrow operators and the Daugavet property for ultraproducts. Positivity 9
, 2005
"... Abstract. We show that if T is a narrow operator (for the definition see below) on X = X1⊕1 X2 or X = X1⊕ ∞ X2, then the restrictions to X1 and X2 are narrow and conversely. We also characterise by a version of the Daugavet property for positive operators on Banach lattices which unconditional sums ..."
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Cited by 15 (10 self)
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Abstract. We show that if T is a narrow operator (for the definition see below) on X = X1⊕1 X2 or X = X1⊕ ∞ X2, then the restrictions to X1 and X2 are narrow and conversely. We also characterise by a version of the Daugavet property for positive operators on Banach lattices which unconditional sums
A Banach space with the Schur and the Daugavet property
 PROC. AMER. MATH. SOC
, 2003
"... We show that a minor refinement of the BourgainRosenthal construction of a Banach space without the RadonNikodym property which contains no bounded δtrees yields a space with the Daugavet property and the Schur property. Using this example we answer some open questions on the structure of such s ..."
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Cited by 11 (7 self)
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We show that a minor refinement of the BourgainRosenthal construction of a Banach space without the RadonNikodym property which contains no bounded δtrees yields a space with the Daugavet property and the Schur property. Using this example we answer some open questions on the structure
NUMERICAL INDEX AND THE DAUGAVET PROPERTY FOR L∞(µ, X)
, 2003
"... We prove that the space L∞(µ, X) has the same numerical index as the Banach space X for every σfinite measure µ. We also show that L∞(µ, X) has the Daugavet property if and only if X has or µ is atomless. ..."
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Cited by 3 (3 self)
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We prove that the space L∞(µ, X) has the same numerical index as the Banach space X for every σfinite measure µ. We also show that L∞(µ, X) has the Daugavet property if and only if X has or µ is atomless.
The Daugavet property of C∗algebras, JB∗triples, and of their isometric preduals
, 2004
"... A Banach space X is said to have the Daugavet property if every rankone operator T: X − → X satisfies ‖Id + T ‖ = 1 + ‖T ‖. We give geometric characterizations of this property in the settings of C ∗algebras, JB ∗triples and their isometric preduals. We also show that, in these settings, the Dau ..."
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Cited by 7 (2 self)
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A Banach space X is said to have the Daugavet property if every rankone operator T: X − → X satisfies ‖Id + T ‖ = 1 + ‖T ‖. We give geometric characterizations of this property in the settings of C ∗algebras, JB ∗triples and their isometric preduals. We also show that, in these settings
Results 1  10
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