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8. Completely bounded maps in the Banach space setting

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1618)

Abstract

In this chapter, we introduce the notion of p-complete boundedness for \(1 \leq p < \infty\). The case p = 2 is the classical one, presented above in chapter 3. In this setting, we extend the fundamental factorization of c.b. maps. We show that the extension property still holds under suitable assumptions. Finally, we apply these results to the similarity problem for homomorphisms in this broader framework.

Mathematics Subject Classification (2000):

  • primary 47AO5
  • 46LO5
  • 43A65 secondary 47A20
  • 47B 10
  • 42B30
  • 46E40
  • 46L57
  • 47C 15
  • 47L20

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Correspondence to Gilles Pisier .

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© 2001 Springer-Verlag Berlin/Heidelberg

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Pisier, G. (2001). 8. Completely bounded maps in the Banach space setting. In: Similarity Problems and Completely Bounded Maps. Lecture Notes in Mathematics, vol 1618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44563-0_9

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  • DOI: https://doi.org/10.1007/978-3-540-44563-0_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41524-4

  • Online ISBN: 978-3-540-44563-0

  • eBook Packages: Springer Book Archive