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An extension of the Riesz-Thorin theorem

Part of the Lecture Notes in Mathematics book series (LNM,volume 604)

Abstract

A version of the Riesz-Thorin theorem is given which enables us to interpolate conditions on a matrix A and on its transpose A′. The following result is typical: if both A and A′ map ℓ2 into ℓ2/3, then A maps ℓ into ℓ1.

Keywords

  • Line Segment
  • Entire Complex Plane
  • Extrapolation Theorem
  • Cardinality Argument
  • Extrapolation Property

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

During the preparation of this paper the author was supported in part by National Science Foundation grant MCS76-06906.

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References

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© 1977 Springer-Verlag

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Bennett, G. (1977). An extension of the Riesz-Thorin theorem. In: Baker, J., Cleaver, C., Diestel, J. (eds) Banach Spaces of Analytic Functions. Lecture Notes in Mathematics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069198

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  • DOI: https://doi.org/10.1007/BFb0069198

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08356-6

  • Online ISBN: 978-3-540-37262-2

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