We study a generalization of relative submajorization that compares pairs positive operators on representation spaces some fixed group. A pair equivariantly relatively submajorizes another if there is an equivariant subnormalized channel takes the components first to satisfying similar positivity constraints as in definition submajorization. In context resource theory approach thermodynamics, t...

In this paper, we use submajorization to compare distances between either multisets of real numbers or multisets modulo translation on the real line. We provide a geometrical interpretation in which multisets are represented by points in an orbifold and bijections between multisets are represented by paths between these points. This interpretation shows that submajorization is closely related t...

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

the aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von neumann algebra on a hilbert space with a normal faithful semi-finite trace $tau$. the submajorization inequalities generalize some results due to zhang, furuichi and lin, etc..

We study refinements between spectral resolutions in an arbitrary II1 factor M and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an application we obtain new characterizations of submajorization and spectral preorder between positive operators in M and new versions of some known inequalities involv...

We prove the Trotter–Kato product formula for arbitrary symmetric F-normed ideals which are closed with respect to logarithmic submajorization. This class of include all quasi-Banach ideals.