Rank-one operators in reflexive one-sided A-submodules

On nest modules of matrices over division rings

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

Factoring Finite-rank Linear Functional Systems∗

By a finite-rank (linear functional) system, we mean a system of linear differential, shift and q-shift operators or, any mixture thereof, whose solution space is finite-dimensional. This poster attempts to develop an algorithm for factoring finite-rank systems into “subsystems” whose solution spaces are of lower dimension. This work consists of three parts: 1. using module-theoretic language t...

Decompositions of Reflexive Bimodules over Maximal Abelian Selfadjoint Algebras

We generalize the notion of ‘diagonal’ from the class of CSL algebras to masa bimodules. We prove that a reflexive masa bimodule decomposes as a sum of two bimodules, the diagonal and a module generalizing the w*-closure of the Jacobson radical of a CSL algebra. The latter module turns out to be reflexive, a result which is new even for CSL algebras. We show that the projection onto the direct ...

On One-Sided Ideals of Rings of Linear Transformations

On the Structure of Ideals of the Dual Algebra of a Coalgebra

The weak-* topology is seen to play an important role in the study of various finiteness conditions one may place on a coalgebra C and its dual algebra C*. Here we examine the interplay between the topology and the structure of ideals of 0*. The basic theory has been worked out for the commutative and almost connected cases (see [2]). Our basic tool for reducing to the almost connected case is ...