Operators Similar to Contractions and Their Similarity to a Normal Operator

2001/11/10 by Stanislav Kupin, Kupin, Stanislav
Mathematics · #47B15 #47B44 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP) #math.CA #math.SP #msc:47B15 #msc:47B44

paper · pdf · doi:10.48550/arxiv.math/0111125

LaTex, 17 pages, preliminary version

arxiv created 2001/11/10 · arxiv updated 2009/11/30

Abstract

It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We obtain results of the same type for a wider (than contractions) class of operators.

Related

• On similarity to contractions of class C_{⋅ 0} with finite defects
• Perturbations of operators similar to contractions and the commutator equation
• A new functional model for contractions
• Does a typical \ℓ_p ,- ,space contraction have a non-trivial\n invariant subspace?
• Reducing subspaces of C₀₀ contractions