If a and b are trace-class operators, and if u is a partial isometry, then \(\), where ∥⋅∥1 denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality.
KeywordsTrace Class Partial Isometry Young Inequality Schmidt Form
Unable to display preview. Download preview PDF.