Original scientific paper

Normality of adjointable module maps

Kamran Sharifi ; Department of Mathematics, Shahrood University of Technology, Shahrood, Iran

Abstract

Normality of bounded and unbounded adjointable operators is discussed. If T is an adjointable
operator on a Hilbert C*-module which has polar
decomposition, then T is normal if and only if there exists a
unitary operator $ \mathcal{U}$ which commutes with T and $T^*$
such that $T=\mathcal{U} \, T^*.$ Kaplansky's theorem for
normality of the product of bounded operators is also reformulated
in the framework of Hilbert C*-modules.

Keywords

Hilbert C*-modules; polar decomposition; normal operators; C*-algebra of compact operators; unbounded operators

Hrčak ID:

82996

URI

https://hrcak.srce.hr/82996

Publication date:

12.6.2012.

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