Smooth measures, the Malliavin calculus and approximations in infinitedimensional spaces
V. I. Bogachev (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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V. I. Bogachev (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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A. Jiménez-Vargas, J. Mena-Jurado, R. Nahum, J. Navarro-Pascual (1999)
Studia Mathematica
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Let X be an infinite-dimensional complex normed space, and let B and S be its closed unit ball and unit sphere, respectively. We prove that the identity map on B can be expressed as an average of three uniformly retractions of B onto S. Moreover, for every 0≤ r < 1, the three retractions are Lipschitz on rB. We also show that a stronger version where the retractions are required to be Lipschitz does not hold.
Appell, Jürgen, Erzakova, Nina A., Santana, Sergio Falcon, Väth, Martin (2004)
Fixed Point Theory and Applications [electronic only]
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R. Ovsepian, A. Pełczyński (1975)
Studia Mathematica
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Victor Klee (1960)
Fundamenta Mathematicae
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M. I. Ostrovskii (1996)
Extracta Mathematicae
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Nigel J. Kalton (2004)
Collectanea Mathematica
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We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 < α < 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if...
Clifford Kottman (1975)
Studia Mathematica
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Godefroy, Gilles (2000)
Serdica Mathematical Journal
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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.