Bilateral weighted shift operators similar to normal operators

2015/06/05 by György Pál Gehér, Gehér, György Pál
Mathematics · #47B15 #47B37 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47B15 #msc:47B37

paper · pdf · doi:10.48550/arxiv.1506.01806

6 pages, Keywords: Bilateral weighted shift operator, similarity to normal operators

arxiv created 2015/06/05 · arxiv updated 2015/06/08

Abstract

We prove that an injective, not necessarily bounded weighted bilateral shift operator on ℓ²(ℤ) is similar to a normal operator if and only if it is similar to a scalar multiple of the simple (i.e. unweighted) bilateral shift operator S.

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