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The parallel sum of nonlinear monotone operators. (English) Zbl 0628.47033
Let H be a Hilbert space with inner product \(<*,.>\) and operators on H are identified with their graphs. A monotone operator A on H is a subset of \(H\times H\) such that for any \([x_ i,y_ i]\in A\), \(i=1,2\), we have \(<y_ 1-y_ 2,x_ 1-x_ 2>\geq 0\). The parallel sum of A and B denoted by A: B is defined by \((A^{-1}+B^{-1})^{-1}.\)
The author discusses algebraic properties of the parallel sums and shows that the class of monotone operators is closed under the operation of parallel sums. The question of determination of the domain of the parallel sum is looked into. A few results are sharpened by considering projections and subdifferentials.
Reviewer: N.K.Thakare

47H05 Monotone operators and generalizations
Full Text: DOI
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