Abstract
Here, we show the equivalent conditions for integrability and being almost everywhere zero of trace-class operator-valued functions with respect to some spectral measure. Furthermore, we investigate the relation between the convergence of these functions and the one of their integrals.
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Notes
The \(C^*\)-algebra of all bounded Borel-measurable complex-valued functions on \(\varOmega \).
The set of all bounded operators on \({\mathbf {B}}({\mathcal {H}})\).
References
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Khosheghbal-Ghorabayi, M., Bagheri-Bardi, GA. E-integrability of trace-class operator-valued functions. Positivity 25, 369–378 (2021). https://doi.org/10.1007/s11117-020-00767-5
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DOI: https://doi.org/10.1007/s11117-020-00767-5