TY  - JOUR
ID  - Fischbacher2021
LB  - Fischbacher2021
AU  - Fischbacher, Christoph
TI  - Extensions of dissipative operators with closable imaginary part
ST  - Extensions of dissipative operators with closable imaginary part
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 3
SP  - 381
EP  - 393
DO  - https://doi.org/10.7494/OpMath.2021.41.3.381
UR  - https://doi.org/10.7494/OpMath.2021.41.3.381
AB  - Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) 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.
KW  - extension theory
KW  - dissipative operators
KW  - ordinary differential operators
SN  - 1232-9274
ER  -