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

2005/04/14 by M. M. Malamud, Mark Malamud, Malamud, Mark
Computer Science · Mathematics · #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:47A57 #msc:47B25

paper · pdf · doi:10.48550/arxiv.math/0504304

arxiv created 2005/04/14 · arxiv updated 2009/12/01

Abstract

A description of the set of m-sectorial extensions of a dual pair \A₁,A₂\ of nonnegative operators is obtained. Some classes of nonaccretive extensions of the dual pair \A₁,A₂\ are described too. Both problems are reduced to similar problems for a dual pair \T₁,T₂\ of nondensely defined symmetric contractions T_j=(I-A_j)(I+A_j)^-1, j∈\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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