Operator Holes and extensions of sectorial operators and dual pairs of contractions

Mark Malamud

paper

Operator Holes and extensions of sectorial operators and dual pairs of contractions

arXiv:math/0504304

Abstract

A description of the set of $m$ -sectorial extensions of a dual pair ${A_{1}, A_{2}}$ of nonnegative operators is obtained. Some classes of nonaccretive extensions of the dual pair ${A_{1}, A_{2}}$ are described too. Both problems are reduced to similar problems for a dual pair ${T_{1}, T_{2}}$ of nondensely defined symmetric contractions $T_{j} = (I - A_{j}) (I + A_{j})^{- 1}, j \in {1, 2}$ . In turn these problems are reduced to the investigation of the corresponding operator "holes". A complete description of the set of all proper and improper extensions of a nonnegative operator is obtained too.