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Convexity conditions for the space of regular operators

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Abstract

In this article we study the following natural questions: When is the quasi-Banach lattice of regular linear operators or homogeneous polynomials between quasi-Banach lattices (p, q)-convex? (p, q)-concave? geometrically convex?

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Acknowledgements

The author would like to thank the reviewer for some valuable remarks and useful suggestions, which led to an improvement of the manuscript.

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Authors and Affiliations

  1. Regional Mathematical Center of Southern Federal University, Bolshaya Sadovaya Str.,105/42, Rostov-on-Don, Russia, 344006

    Zalina Kusraeva

  2. Southern Mathematical Institute of Vladikavkaz Scientific Center of Russian Academy of Sciences, Markus Str., 22, Vladikavkaz, Russia, 362027

    Zalina Kusraeva

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  1. Zalina Kusraeva
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Correspondence to Zalina Kusraeva.

Additional information

The study was supported by Russian Foundation for Basic Research (Project No. 18-31-00205).

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Kusraeva, Z. Convexity conditions for the space of regular operators. Positivity 23, 445–459 (2019). https://doi.org/10.1007/s11117-018-0616-z

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  • DOI: https://doi.org/10.1007/s11117-018-0616-z

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