Abstract
The basic properties of the parallel sum were developed for nonnegative matrices in finite-dimensional spaces. However, without suitable restrictions, very little of the preceding theories will hold for bounded linear operators A and B acting in Hilbert space. In this paper, generalization to non-selfadjoint operators is considered and various properties of parallel sum A:B=A(A+B)†B are given. Meanwhile, the common upper and lower bounds of positive operators by using the parallel sum are given and some relationships between the parallel sum of projection operators are obtained.
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