On $$\pmb {\mathcal {U}}$$ U -weak stability of coarse isometries between $$\pmb {L^p}$$ L p spaces

Quanqing Fang (), Duanxu Dai () and Jichao Zhang ()
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Quanqing Fang: Putian University
Duanxu Dai: Jimei University
Jichao Zhang: Hubei University of Technology

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 843-848

Abstract: Abstract In this paper, we study $${\mathcal {U}}$$ U -stability and weak $${\mathcal {U}}$$ U -stability of coarse isometries between Banach spaces for a free ultrafilter $${\mathcal {U}}$$ U on $${\mathbb {N}}$$ N . As a result, for a coarse isometry $$f:L_p(\Omega _1,\Sigma _1,\mu _1)\rightarrow L_p(\Omega _2,\Sigma _2,\mu _2)$$ f : L p ( Ω 1 , Σ 1 , μ 1 ) → L p ( Ω 2 , Σ 2 , μ 2 ) ( $$1

Keywords: $$L^p$$ L p space; Coarse isometry; Linear isometry; $${\mathcal {U}}$$ U -weak stability; Primary 46B04; 46B20; 47A58; Secondary 46A20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00178-6

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