Silbermann, B.

function idempotent invertible algebra logarithmic invertible values logarithmic residues residue example banach value theorem family matrix operator banach algebra factor origin identity order trace point element lrleft situation right proof annihilating section logarithmic residue lrright representation laurent expansion function f number ehrhardt polynomial · · · matrix representations proposition resolvent silbermann space e − qm non-zero idempotents p 1 result fredholm operator cauchy domain product divisor integer argument domain subset non-empty theory right logarithmic residue fredholm expansion banach algebras unital banach algebra ficient unit element application suf ficient family projection meromorphic matrice property definition fi nite number banach algebra b 1945–1965 laurent function g coefficient resolvent f j-invertible hilbert space