Abstract
The Mazur intersection property (MIP, for short) was introduced in Definition 262, that we repeat here: The norm k · k of a Banach space X is said to have the Mazur intersection property (MIP) if each bounded closed convex set in X is the intersection of closed balls. We give below only a list of some basic results in this area. In the 40’s, Mazur proved that any Fréchet differentiable norm on a reflexive space has the MIP. Since then this concept got a wide use in the Banach space theory and elsewhere (for instance in operator theory). It is favored for its elegance and usefulness.
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Guirao, A.J., Montesinos, V., Zizler, V. (2022). Norms with the Mazur intersection Property. In: Renormings in Banach Spaces. Monografie Matematyczne, vol 75. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-08655-7_33
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DOI: https://doi.org/10.1007/978-3-031-08655-7_33
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-08654-0
Online ISBN: 978-3-031-08655-7
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