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

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

2005-04-14

arxiv.org/abs/math/0504304v1

Mathematics

Functional Analysis

Scientific paper

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.

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