Mehdi Radjabalipour

A nil algebra of bounded operators on Hilbert space with semisimple norm closure

An algebra of operators having the property of the title is constructed and it is used to give examples related to some recent invariant subspace results.

On invariant operator ranges

A matricial representation is given for the algebra of operators leaving a given dense operator range invariant. It is shown that every operator on an infinite-dimensional Hilbert space has an uncountable family of invariant operator ranges, any two of which intersect only in (0).

On semigroups of matrices with traces in a subfield

Abstract It is shown that an irreducible semigroup of n × n complex matrices with real spectra is simultaneously similar to a semigroup of real matrices. Weaker results are obtained for semigroups of matrices over a general field with traces in a subfield.

On Rings of Matrices Over Division Rings

Let be a subring of Mn (D) for some division ring D satisfying the following three conditions: (i) there exists a division subring K of D such that for all a ∈ K and all ; (ii) for every , there exist ; and (iii) A = 0 if . It is shown that contains a maximal central idempotent C such that , and if E in in the center of are minimal and is a division ring and . As a corollary, we extend a result due to Omladič–Radjabalipour–Radjavi for K-algebras generated by unital semigroups of n × n matrices with entries in a field D and traces in a subfield K.

Commutators of small rank and reducibility of operator semigroups

It is easy to see that if

Equivalence of decomposable and

\cG

2

is a non-abelian group of unitary matrices, then for no members

-decomposable operators.

A

Towards a classification of maximal unicellular bands

and

Principal-ideal Bands

B