A logarithmic residue is a contour integral of the (left or right) logarithmic derivative of an analytic Banach algebra valued function. Logarithmic residues are intimately related to sums of idempotents. The present paper is concerned with logarithmic residues and sums of idempotents in the...

A logarithmic residue is a contour integral of a logarithmic derivative (left or right) of an analytic Banach algebra valued function. For functions possessing a meromorphic inverse with simple poles only, the logarithmic residues are identified as the sums of idempotents. With the help of this...

An analysis is presented of the circumstances under which, by the extraction of elementary factors, an analytic Banach algebra valued function can be transformed into one taking invertible values only. Elementary factors are generalizations of the simple scalar expressions λ – α,...