Partial orders based on core-nilpotent decomposition

Partial Orders on Partial Isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spac...

The space of bi-invariant orders on a nilpotent group

We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it is a Cantor set if G is countable), and give examples to show that the outer automorphism group of G does not always act faithfully on this space. Also, it ...

Partial orders in rings based on generalized inverses – unified theory

Article history: Received 20 August 2014 Accepted 3 January 2015 Available online xxxx Submitted by Y. Wei MSC: 06A06 15A09 16U99

Revising Partial Pre-Orders with Partial Pre-Orders: A Unit-Based Revision Framework

Belief revision studies strategies about how agents revise their belief states when receiving new evidence. Both in classical belief revision and in epistemic revision, a new input is either in the form of a (weighted) propositional formula or a total pre-order (where the total pre-order is considered as a whole). However, in some real-world applications, a new input can be a partial pre-order ...

Extending Partial Orders to Dense Linear Orders