Extremal maximal sectorial extensions of sectorial relations

The extremal maximal sectorial extensions of a not necessarily densely defined sectorial relation (multivalued linear operator) in a Hilbert space are characterized in terms of a construction which goes back to Sebestyen and Stochel. In particular the two extreme maximal sectorial extensions, namely the Friedrichs extension and the Krein extension, are characterized. For this purpose a survey is given of the connection between closed sectorial forms and maximal sectorial relations. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.