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Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 781–800 | Cite as

Maximal Operators with Respect to the Numerical Range

  • Rosario CorsoEmail author
Article
  • 68 Downloads

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.

Keywords

Numerical range Maximal operators Sector Strip Sesquilinear forms Strongly continuous semi-groups Cayley transform 

Mathematics Subject Classification

Primary 47A20 Secondary 47A12 47B44 47A07 

Notes

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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di PalermoPalermoItaly

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