Majorization and singular values. III (Q1174312)

[For part I and II see Linear Multilinear Algebra 21, 211-214 (1987; Zbl 0651.15014) and SIAM J. Matrix Anal. Appl. 10, No. 4, 429-434 (1989; Zbl 0686.15006).] Some majorization inequalities are obtained which relate the singular values of a complex square matrix from the corresponding space and those of the complex square matrix obtained by an arbitrary linear map on this space. A particularly simple form of the inequalities holds for any positive map. Using the arbitrary linear maps permits the presentation of the results in a unified manner.