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Geometry of the Marcinkiewicz Sequence Space

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Abstract

We characterise the real extreme points of the unit ball of \(m^0_\Psi \), the complex extreme points of the unit ball of \(m_\Psi \) and the real extreme and exposed points of the unit ball of \((m_\Psi ^0)'\). Using these characterisations we show that, depending on the length of the extreme points, the multipliers of \(m^0_\Psi \) are either constant multiple of the identity or diagonal operators.

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Acknowledgements

The authors would like to thank the referee for his/her careful reading of the original version of the paper. This project was partially supported by PAI-UdeSA 2013, CONICET-PIP 0483, ANPCyT PICT 2011-1456 and UBACyT 1-474. Part of this work was developed while the first author visited the Department of Mathematics, Universidad de San Andrés and when the second author visited the School of Mathematics and Statistics, University College Dublin. Each wishes to thanks the hospitality they received in the respective institutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland

    Christopher Boyd

  2. Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina

    Silvia Lassalle

  3. IMAS–CONICET, Buenos Aires, Argentina

    Silvia Lassalle

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  1. Christopher Boyd
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  2. Silvia Lassalle
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Correspondence to Christopher Boyd.

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Boyd, C., Lassalle, S. Geometry of the Marcinkiewicz Sequence Space. J Geom Anal 31, 5336–5354 (2021). https://doi.org/10.1007/s12220-020-00480-5

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  • DOI: https://doi.org/10.1007/s12220-020-00480-5

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