The Proper Dissipative Extensions of a Dual Pair

2016/03/27 by Fischbacher, Christoph, Naboko, Sergey, Wood, Ian · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1603.08192

Abstract

Let A and (-\widetildeA) be dissipative operators on a Hilbert space H and let (A,\widetildeA) form a dual pair, i.e. A⊂\widetildeA^*, resp. \widetildeA⊂ A^*. We present a method of determining the proper dissipative extensions \widehatA of this dual pair, i.e. A⊂ \widehatA⊂\widetildeA^* provided that D(A)\capD(\widetildeA) is dense in H. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions.

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• Complete Non-Selfadjointness of Extensions of Symmetric Operators with Bounded Dissipative Perturbations

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