Logarithmic residues in the Banach algebra generated by the compact operators and the identity

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 in a specific Banach algebra, namely the one generated by the compact operators and the identity in the case when the underlying Banach space is infinite dimensional. The situation is more complex than encountered in previous investigations concerning logarithmic residues. Logarithmic derivatives may have essential singularities and the geometric properties of the Banach space play a role. Topological properties of the set of logarithmic residues are considered too.

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