Integral Equations and Operator Theory

, Volume 32, Issue 1, pp 65–74

Toeplitz operators with noncommuting symbols

  • Michael Marsalli
  • Graeme West
Article

Abstract

LetM be a von Neumann algebra with a faithful normal tracial state τ and letH be a finite maximal subdiagonal subalgebra ofM. LetH2 be the closure ofH in the noncommutative Lebesgue spaceL2(M). We consider Toeplitz operators onH2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH2(\(\mathbb{T}\)) with symbol fromL(\(\mathbb{T}\)), including norm estimates, a Hartman-Wintner spectral inclusion theorem, and a characterisation of the weak* continuous linear functionals on the space of Toeplitz operators.

1991 Mathematics Subject Classification

primary 46L50 47B35 secondary 47A12 

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Copyright information

© Birkhäuser Verlag 1998

Authors and Affiliations

  • Michael Marsalli
    • 1
  • Graeme West
    • 2
  1. 1.Mathematics DepartmentIllinois State UniversityNormalUSA
  2. 2.Mathematics DepartmentUniversity of the WitwatersandSouth Africa

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