An extension of results of A. McD. Mercer and I. Gavrea.
Kantorovich type inequalities for ordered linear spaces.
On Schur-Ostrowski type theorems for group majorizations.
Upper bounds on certain functionals defined on groups of linear operators.
A review of selected topics in majorization theory
In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors...
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