Isometries of non-self-adjoint operator algebras

Homology for Operator Algebras II : Stable Homology for Non-self-adjoint Algebras

A new homology is defined for a non-self-adjoint operator algebra with a distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra. Under natural hypotheses the zeroth order group coincides with the K0 group of the generated C ∗-algebra. Several identifications and applications are given, and in particular it is shown how ...

Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator

We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of ...

Spectral Behaviour of a Simple Non-self-adjoint Operator

We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d2/dx2 ⊗ A acting on L(0, 1) ⊗ C, where A is a 2 × 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of [0, 1] ⊂ R. For A ∈ R we explore in detail the connection between the entries of A and the spectrum of AD, we find necessary c...

Nonself-adjoint operator algebras for dynamical systems

This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.

The Laplace operator is essentially self-adjoint