The Daugavet Property of the Space of Lipschitz Functions
نویسنده
چکیده
where Id is the identity operator on C[0, 1]. This equation is now called Daugavet equation. The Banach space X is said to have the Daugavet property when all compact operators on X satisfy the Daugavet equation. More information about the Daugavet spaces can be found in [Werner, 2001]. In the same paper was also posed the question, whether the Banach space of Lipschitz functions on unit square possesses the Daugavet property. We will prove that the answer is positive (see Theorem 4). We will also prove the similar result for the Banach space of continuously differentiable functions on a closure of some bounded domain in R (see Theorem 7).
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