Abstract
LetM be a von Neumann algebra with a faithful normal tracial state τ and letH ∞ be a finite maximal subdiagonal subalgebra ofM. LetH 2 be the closure ofH ∞ in the noncommutative Lebesgue spaceL 2(M). We consider Toeplitz operators onH 2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH 2(\(\mathbb{T}\)) 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.
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Marsalli, M., West, G. Toeplitz operators with noncommuting symbols. Integr equ oper theory 32, 65–74 (1998). https://doi.org/10.1007/BF01193507
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DOI: https://doi.org/10.1007/BF01193507