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The existence of linear selection and the quotient lifting property

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Abstract

Lifting properties for Banach spaces are studied. An alternate version of the lifting property due to Lindenstrass and Tzafriri leads to a new geometric property called the quotient lifting property for pairs of Banach spaces (X, J), with J proximinal in X. Several necessary and sufficient conditions for the property to hold are given.

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Acknowledgements

The authors are grateful to Jesús Suárez, Amin Sofi, and TSSRK Rao for helpful comments. The authors are also grateful to the referee for several suggestions that improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Memphis, Memphis, TN, 38152-3240, USA

    Monika & Fernanda Botelho

  2. Central Michigan University, Mount Pleasant, Michigan, USA

    Richard Fleming

Authors
  1. Monika
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  2. Fernanda Botelho
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  3. Richard Fleming
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Corresponding author

Correspondence to Fernanda Botelho.

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Communicated by Jaydeb Sarkar.

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Monika, Botelho, F. & Fleming, R. The existence of linear selection and the quotient lifting property. Indian J Pure Appl Math 53, 774–781 (2022). https://doi.org/10.1007/s13226-021-00171-z

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  • DOI: https://doi.org/10.1007/s13226-021-00171-z

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