One-sided star partial orders for bounded linear operators
Jānis Cı̄rulis · Operators and Matrices · 2015
We compare some recent approaches to transferring the notions of left-and rightstar partial order, introduced for complex matrices in early 90-ies, to bounded linear Hilbert space operators, and discuss a new version of these orders. The main results state that every initial segment of B(H) under the (new) left-star order is a complete orthomodular sublattice isomorphic to an initial segment of the lattice of closed subspaces of the underlying Hilbert space H . We also associate a certain orthogonality relation with the order.