We use a weighted analogue of a trace to define a weighted non-commutative decreasing rearrangement and show its relationship with the singular value function. We further show an alternative approach… Click to show full abstract
We use a weighted analogue of a trace to define a weighted non-commutative decreasing rearrangement and show its relationship with the singular value function. We further show an alternative approach to constructing weighted non-commutative Banach function spaces using weighted non-commutative decreasing rearrangements and prove that this approach is equivalent to the original approach by Labuschagne and Majewski.
               
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