Essentially Normal Operator + Compact Operator = Strongly Irreducible Operator

Irreducible Representations of Operator Algebras

The Laplace operator is essentially self-adjoint

Irreducible Positive Linear Maps on Operator Algebras

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...

Operator Theory and Operator Algebras

Operator programs and operator processes

We define a notion of program which is not a computer program but an operator program: a detailed description of actions performed and decisions taken by a human operator (computer user) performing a task to achieve a goal in a simple setting consisting of that user, one or more computers and a work environment. Our definition and notations are based on the program algebra PGA: a small body of ...