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Some functorial properties of Schatten classes

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Abstract

In this paper, we begin with the study of elements in \(C^*\)-algebras which are mapped to Schatten class ideals through the faithful left regular representation. We further give some functorial properties of Schatten classes on the category of representations of a \(C^*\)-algebra and category of unitary representations of a group.

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Notes

  1. This proof is motivated by the idea provided by Prof. Martin Argerami.

References

  1. Castillo, J.M.: The Hitchhiker guide to categorical banach space theory. Extract. Math. 25(2), 103–149 (2010)

    MathSciNet  MATH  Google Scholar 

  2. Castillo, J., Moreno, Y.: The category of exact sequences of Banach spaces. In: Castillo, J., Johnson, W. (eds.) Methods in Banach Space Theory (London Mathematical Society Lecture Note Series), pp. 139–158. Cambridge University Press, Cambridge (2006)

    Chapter  Google Scholar 

  3. Chung, K.L.: A Course in Probability Theory. Academic Press, London (1974)

    MATH  Google Scholar 

  4. Folland, G.B.: A Course in Abstract Harmonic Analysis. Taylor & Francis group, Boca Raton (2016)

    Book  Google Scholar 

  5. Kremnizer, K., Smith, C.: A Tannakian Reconstruction Theorem for IndBanach Spaces arXiv:1703.05679 [math.FA]

  6. Murphy, J.J.: C*-Algebras and Operator Theory. Academic Press, London (2014)

    Google Scholar 

  7. Palmer, T.W.: Banach Algebras and the General Theory of \(*\)-Algebras, p. 2. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

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Acknowledgements

We would like to thank the reviewers for pointing out the mistakes and suggesting appropriate changes. The research work presented here was jointly carried out by the authors while being funded by Council of Scientific and Industrial Research-Government of India and University Grants Commission-Government of India.

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Authors and Affiliations

  1. School of Physical Sciences, J.N.U, New Delhi, India

    Lav Kumar Singh

  2. Dr. Harisingh Gour Central University, Sagar, MP, India

    A. K. Verma

Authors
  1. Lav Kumar Singh
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  2. A. K. Verma
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Correspondence to Lav Kumar Singh.

Additional information

Communicated by Chi-Keung Ng.

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Singh, L.K., Verma, A.K. Some functorial properties of Schatten classes. Adv. Oper. Theory 5, 1406–1413 (2020). https://doi.org/10.1007/s43036-020-00049-7

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  • DOI: https://doi.org/10.1007/s43036-020-00049-7

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