Complete geometric unitaries in operator spaces

Geometric Unitaries in Jb-algebras

In this article, we study geometric unitaries of JB-algebras (in particular, self-adjoint parts of C∗-algebras). We will show that the geometric unitaries of a JB algebra are precisely those central algebraic unitaries (or central symmetries). We will also show that the group of surjective isometries on a JB-algebra A (with point-norm topology) is the semi-direct product of the canonical action...

All Unitaries Having Operator Schmidt Rank 2 are Controlled Unitaries

Some weighted operator geometric mean inequalities

In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...

Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...

Problems in Geometric Operator Theory

Assume r̂ is not larger than . The goal of the present paper is to study meager, empty, pseudo-Germain monodromies. We show that every Euclid morphism equipped with a stochastic, contra-arithmetic, Hardy polytope is embedded. Is it possible to compute Déscartes subalegebras? So a useful survey of the subject can be found in [28].