Logarithmic Residues of Fredholm Operator Valued Functions and Sums of Finite Rank Projections
Harm Bart, Torsten Ehrhardt, Bernd Silbermann · Birkhäuser Basel eBooks · 2002
Logarithmic residues of analytic Fredholm operator valued functions are identified as sums of finite rank projections. The set of all such sums is closed and the restriction of the trace to it is continuous; its connected components are determined by the (integer) values of the trace. Two finite rank bounded linear operators can be written as the left and right logarithmic residues of a single Fredholm operator valued function if and only if they belong to the same connected component, i.e., if and only if they are sums of finite rank projections having the same trace. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.