Edward Poon

Linear operators preserving directional majorization

Abstract A characterization of linear operators preserving directional majorization is given. The result extends a theorem of T. Ando [Linear Algebra Appl. 118 (1989) 163], and the proof also gives the characterization of linear operators preserving multivariate majorization recently obtained by Beasley and Lee.

Physical transformations between quantum states

Given two sets of quantum states {A1, …, Ak} and {B1, …, Bk}, represented as sets as density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a trace-preserving completely positive map, such that T(Ai) = Bi for i = 1, …, k. General completely positive maps without the trace-preserving requirement, and unital completely positive maps transforming the states are also considered.

MAPS PRESERVING SPECTRAL RADIUS, NUMERICAL RADIUS, SPECTRAL NORM ∗

Characterizations are obtained for Schur (Hadamard) multiplicative maps on com- plex matrices preserving the spectral radius, numerical radius, or spectral norm. Similar results are obtained for maps under weaker assumptions. Furthermore, a characterization is given for maps f satisfyingA ◦ B� = � f(A) ◦ f(B)� for all matrices A and B.

Additive Decomposition of Real Matrices

The orthogonal orbit

Entanglement transformation between sets of bipartite pure quantum states using local operations

{\cal O}(A)

ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME

of an n × n real matrix A is the set of real matrices of the form

Induced norms, states, and numerical ranges

P^t \ AP

A Generalization of Complete Reducibility

where

Continuous multiplicative maps of Toeplitz algebras

P^t P = I_n

Multiplicative Sets of Primitive Idempotents and Primitive Ideals

. We show that