## Abstract We introduce the notion of an __m__โisometry 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__โisometries, showing that they are never __N__โs
On isometries in Lp spaces
โ 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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๐ SIMILAR VOLUMES
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.
## Abstract Boundedness of oneโsided maximal functions, singular integrals and potentials is established in __L__(__I__) spaces, where __I__ is an interval in **R**. (ยฉ 2008 WILEYโVCH Verlag GmbH & Co. KGaA, Weinheim)
## Abstract We present bounded positivity preserving operators from __L__~__p__~(โ) to __L__~__q__~ (__โ__), for 1 < __p__ < โ, 1/pโ1/q < 1/2, which are not integral operators.