Isolated points of the spectra of conservative matrices

Abstract

ABSTRACT. We show that the only possible isolated points in the spectrum of a conservative triangular matrix are its diagonal elements, and that any Hausdorff method corresponding to an absolutely continuous mass function is in the norm closure of the analytic methods.

Hausdorff Prime Matrices

“…It then follows that f ∈ H(G), and f is continuous and bounded on G in C. Let σ(H µ ) denote the spectrum of H µ . Sharma [9] has shown that σ(H f ) ⊃ f (G). Either 0 ∈ σ(H f ) or 0 / ∈ σ(H f ).…”