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On isometries in Lp spaces

โœ Scribed by Juan Carlos Merlo


Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
147 KB
Volume
15
Category
Article
ISSN
0001-8708

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## Abstract We introduce the notion of an __m__โ€isometry of a Banach space, following a definition of Agler and Stankus in the Hilbert space setting. We give a first approach to the general theory of these maps. Then, we focus on the dynamics of __m__โ€isometries, showing that they are never __N__โ€s

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We extend Maurey's theorem on the existence of a fixed point for an isometry of a nonempty closed bounded convex subset of a superreflexive space to obtain the existence of common fixed points for countable families of commuting isometries.

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## Abstract Boundedness of oneโ€sided maximal functions, singular integrals and potentials is established in __L__(__I__) spaces, where __I__ is an interval in **R**. (ยฉ 2008 WILEYโ€VCH Verlag GmbH & Co. KGaA, Weinheim)

Invariant Subspaces of Operators on lp-S
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## Abstract We present bounded positivity preserving operators from __L__~__p__~(โ„) to __L__~__q__~ (__โ„__), for 1 < __p__ < โˆž, 1/pโ€1/q < 1/2, which are not integral operators.