Some conditions implying normality of operators

Details Some conditions implying normality of operators Some conditions implying normality of operators

2011-06-15

arxiv.org/abs/1106.3058v1

C. R. Math. Acad. Sci. Paris 349 (2011), no. 5-6, 251-254

Mathematics

Functional Analysis

Scientific paper

Let $T\in\mathbb{B}(\mathscr{H})$ and $T=U|T|$ be its polar decomposition. We
proved that (i) if $T$ is log-hyponormal or $p$-hyponormal and $U^n=U^\ast$ for
some $n$, then $T$ is normal; (ii) if the spectrum of $U$ is contained in some
open semicircle, then $T$ is normal if and only if so is its Aluthge transform
$\widetilde{T}=|T|^{1\over2}U|T|^{1\over2}$.

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