Abstract
In this chapter, we prove (actually three times) von Neumann’s inequality and its extension (due to Ando) for two mutually commuting contractions. We discuss the case of n > 2 mutually commuting contractions. We introduce the notion of semi-invariance. Finally, we show that Hilbert spaces are the only Banach spaces satisfying von Neumann’s inequality.
Mathematics Subject Classification (2000):
- primary 47AO5
- 46LO5
- 43A65 secondary 47A20
- 47B 10
- 42B30
- 46E40
- 46L57
- 47C 15
- 47L20
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© 2001 Springer-Verlag Berlin/Heidelberg
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Pisier, G. (2001). 1. Von Neumann’s inequality and Ando’s generalization. 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_2
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DOI: https://doi.org/10.1007/978-3-540-44563-0_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41524-4
Online ISBN: 978-3-540-44563-0
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