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

Author

Listed:
  • Quanqing Fang

    (Putian University)

  • Duanxu Dai

    (Jimei University)

  • Jichao Zhang

    (Hubei University of Technology)

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

Suggested Citation

  • Quanqing Fang & Duanxu Dai & Jichao Zhang, 2022. "On $$\pmb {\mathcal {U}}$$ U -weak stability of coarse isometries between $$\pmb {L^p}$$ L p spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 843-848, December.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:4:d:10.1007_s13226-021-00178-6
    DOI: 10.1007/s13226-021-00178-6
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    References listed on IDEAS

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    1. Duanxu Dai, 2018. "Stability of basic sequences via nonlinear ε-isometries," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(3), pages 571-579, September.
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