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arXiv · 2012.12920

Extensions of dissipative operators with closable imaginary part

Christoph Fischbacher
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Abstract

Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.

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Christoph Fischbacher. 2020-12-23. Extensions of dissipative operators with closable imaginary part. https://arxiv.org/abs/2012.12920

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