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Positive-Defininte Functions on Free Semigroups

Published online by Cambridge University Press:  20 November 2018

Gelu Popescu
Gelu Popescu*
Affiliation:
Gelu Popescu Division of Mathematics and Statistics, The University of Texas at San Antonio San Antonio, TX 78249 U.S.A., e-mail: gpopescu@ringer.cs.utsa.edu
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Abstract

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An extension of the Naimark dilation theorem [N], [SzF2] to positive-definite functions on free semigroups is given. This is used to extend the operatorial trigonometric moment problem [A] to a non-commutative setting and to characterize the classes 𝐶ρ (ρ > 0) of all n-tuples of operators that have a p-isometric dilation (see [SzF2] for the case n = 1). It is also shown that 𝐶ρ ⊂ 𝐶ρ′ and 𝐶ρ ≠ 𝐶ρ′ for 0 < ρ < ρ′ < ∞.

The von Neumann inequality [vN], [Po2] is extended to the classes 𝐶p. This is used to prove that any element in 𝐶ρ is simultaneously similar to an element in 𝐶1.

Keywords

47A2047A4547A57
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 887 - 896
Copyright
Copyright © Canadian Mathematical Society 1996

References

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