Let n be a nonempty, proper, convex subset of C. The n-maximal operators are defined as the operators having numerical ranges in n and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the n-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
Corso R. (2019). Maximal Operators with Respect to the Numerical Range. COMPLEX ANALYSIS AND OPERATOR THEORY, 13(3), 781-800 [10.1007/s11785-018-0805-6].
Maximal Operators with Respect to the Numerical Range
Corso R.
2019-01-01
Abstract
Let n be a nonempty, proper, convex subset of C. The n-maximal operators are defined as the operators having numerical ranges in n and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the n-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.
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