Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Abstract

Let be a Hilbert space with the unit operator . The paper deals with the pencil , where and are Hilbert–Schmidt operators in . We suggest a norm estimate for the inverse of . By that estimate, bounds for the spectra of are established and perturbations by bounded operators are investigated. Applications to boundary value problems are also discussed.

Keywords:

• linear operator pencil
• inverse operator
• spectrum

AMS Subject Classifications:

• 47A56
• 47A10
• 47A75