Abstract
In this paper we shall prove that, if S 1, …, S m and T 1, …, T n are sets of commuting contractions on a Hilbert space, both satisfy the von Neumann inequality “in the strong sense”, each S j double commutes with every T k , and, S 1, …, S m generate a nuclear C n-algebra, then the set S 1, …, S m , T 1, …, T n satisfies the von Neumann inequality “in the strong sense”. This gives a new condition for a set of contractions to admit a simultaneous strong unitary dilation.
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© 1992 Springer Basel AG
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Okayasu, T. (1992). The von Neumann Inequality and Dilation Theorems for Contractions. In: Ando, T., Gohberg, I. (eds) Operator Theory and Complex Analysis. Operator Theory: Advances and Applications, vol 59. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8606-2_14
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DOI: https://doi.org/10.1007/978-3-0348-8606-2_14
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9699-3
Online ISBN: 978-3-0348-8606-2
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