Majorizations for generalized s-numbers in semifinite von Neumann algebras (Q1079784)

Some majorizations are established for the generalized s-numbers and the spectral scales of \(\tau\)-measurable operators affiliated with a semifinite von Neumann algebra. When the von Neumann algebra is a matrix algebra, those are the most important majorizations for the singular values and the eigenvalues of matrices (the Lidskii-Wielandt theorem). The proof based on the real interpolation method is quite simple. Some norm inequalities for the noncommutative Lebesgue-Lorentz spaces are derived from the majorizations.