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Maximal Operators with Respect to the Numerical Range

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Abstract

Let \(\mathfrak {n}\) be a nonempty, proper, convex subset of \(\mathbb {C}\). The \(\mathfrak {n}\)-maximal operators are defined as the operators having numerical ranges in \(\mathfrak {n}\) 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 \(\mathfrak {n}\)-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.

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Acknowledgements

This work was supported by the project “Problemi spettrali e di rappresentazione in quasi *-algebre di operatori”, 2017, of the “National Group for Mathematical Analysis, Probability and their Applications” (GNAMPA – INdAM).

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  1. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Rosario Corso

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  1. Rosario Corso
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Correspondence to Rosario Corso.

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Communicated by Daniel Aron Alpay.

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Corso, R. Maximal Operators with Respect to the Numerical Range. Complex Anal. Oper. Theory 13, 781–800 (2019). https://doi.org/10.1007/s11785-018-0805-6

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