Minimal extension of a pseudoresolvent

E. V. Cheremnikh

Lviv Polytechnic National University

Abstract: In a Hilbert space we consider a pseudoresolvent whose range is the whole space. We introduce a set of associated operators which are compatible with the pseudoresolvent in the same way that an operator is compatible with its resolvent. For each associated operator we construct an extension whose resolvent is an extension of the pseudoresolvent and is minimal in a certain sense.

UDC: 517.9

Received: 10.12.1972

 English version: Mathematical Notes, 1973, 14:1, 610–612

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