Abstract
We present a new approach to non-commutative Yosida-Hewitt decompositions in the setting of normed \( \mathcal{M} \)-bimodules of τ-measurable operators affiliated with a semifinite von Neumann algebra \( \mathcal{M} \). Our principal theorem permits the systematic study of the lienar spaces of normal and singular linear functionals on symmetrically normed \( \mathcal{M} \)-bimodules. We present some applications and give a decomposition into normal and singular parts for weakly compact operators on such spaces.
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Dodds, P.G., de Pagter, B. (2009). Non-commutative Yosida-Hewitt Theorems and Singular Functionals in Symmetric Spaces of τ-measurable Operators. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_17
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DOI: https://doi.org/10.1007/978-3-0346-0211-2_17
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