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17
The Daugavet equation for polynomials
 Studia Math
"... Abstract. In this paper we study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality ‖Id + P ‖ = 1 + ‖P‖ is satisfied for all weakly compact polynomials P: X − → X. We show that this is the case when X = C(K), the real or complex space ..."
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Cited by 4 (2 self)
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Abstract. In this paper we study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality ‖Id + P ‖ = 1 + ‖P‖ is satisfied for all weakly compact polynomials P: X − → X. We show that this is the case when X = C(K), the real or complex space
Essential disjointness and the Daugavet equation
 Houston J. Math
, 1993
"... ABSTRACT. When/1 is an extremally disconnected compact Hausdorff space, the space C(/1) is Dedekind complete. Consequently, the space of all order bounded operators on C(/1) is a Dedekind complete Ba•ach lattice (see [5]). Hence, the order disjointhess of two arbitraxy operators is defined in œ•,(C( ..."
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Cited by 3 (0 self)
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corollary of this result states that T satisfies the Daugavet equation (Definition 1.1). This generMizes a result of J. Holub [16], which
THE LARGEST LINEAR SPACE OF OPERATORS SATISFYING THE DAUGAVET EQUATION IN L1
"... Abstract. We find the largest linear space of bounded linear operators on L1(Ω) that, being restricted to any L1(A), A ⊂ Ω, satisfy the Daugavet equation. 1. ..."
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Abstract. We find the largest linear space of bounded linear operators on L1(Ω) that, being restricted to any L1(A), A ⊂ Ω, satisfy the Daugavet equation. 1.
The Daugavet equation for operators not fixing a copy of C[0, 1
 J. Operator Theory
, 1998
"... Abstract. We prove the norm identity ‖Id+T ‖ = 1+‖T‖, which is known as the Daugavet equation, for operators T on C(S) not fixing a copy of C[0, 1], where S is a compact Hausdorff space without isolated points. ..."
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Cited by 4 (3 self)
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Abstract. We prove the norm identity ‖Id+T ‖ = 1+‖T‖, which is known as the Daugavet equation, for operators T on C(S) not fixing a copy of C[0, 1], where S is a compact Hausdorff space without isolated points.
The Daugavet equation for operators not fixing a copy of C(S)
, 1996
"... Abstract. We prove the norm identity ‖Id + T ‖ = 1 + ‖T ‖, which is known as the Daugavet equation, for operators T on C(S) not fixing a copy of C(S), where S is a compact metric space without isolated points. 1. ..."
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Abstract. We prove the norm identity ‖Id + T ‖ = 1 + ‖T ‖, which is known as the Daugavet equation, for operators T on C(S) not fixing a copy of C(S), where S is a compact metric space without isolated points. 1.
The largest linear space of operators satisfying the Daugavet Equation in L1
, 1999
"... We find the largest linear space of bounded linear operators on L1(Ω) that being restricted to any L1(A), A ⊂ Ω, satisfy the Daugavet equation. 1 Introduction. Let (Ω, Σ, µ) be an arbitrary measure space without atoms of infinite measure. Let also Σ + = {A ∈ Σ: µ(A)> 0}. If A ∈ Σ +, L1(A) stands ..."
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Cited by 1 (0 self)
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We find the largest linear space of bounded linear operators on L1(Ω) that being restricted to any L1(A), A ⊂ Ω, satisfy the Daugavet equation. 1 Introduction. Let (Ω, Σ, µ) be an arbitrary measure space without atoms of infinite measure. Let also Σ + = {A ∈ Σ: µ(A)> 0}. If A ∈ Σ +, L1(A) stands
An elementary approach to the Daugavet equation, in: Interaction between Functional Analysis, Harmonic Analysis and Probability
 Lecture Notes in Pure and Appl. Math. 175
, 1994
"... Abstract. Let T : C(S) → C(S) be a bounded linear operator. We present a necessary and sufficient condition for the socalled Daugavet equation Id + T = 1 + T to hold, and we apply it to weakly compact operators and to operators factoring through c 0 . Thus we obtain very simple proofs of results b ..."
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Cited by 14 (3 self)
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Abstract. Let T : C(S) → C(S) be a bounded linear operator. We present a necessary and sufficient condition for the socalled Daugavet equation Id + T = 1 + T to hold, and we apply it to weakly compact operators and to operators factoring through c 0 . Thus we obtain very simple proofs of results
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
Results 1  10
of
17