Normality of adjointable module maps

Details Normality of adjointable module maps Normality of adjointable module maps

2010-11-06

arxiv.org/abs/1011.1582v2

Mathematics

Operator Algebras

8 pages / corrected typos, references updated

Scientific paper

Normality of bounded and unbounded adjointable operators are discussed. Suppose $T$ is an adjointable operator between Hilbert C*-modules 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.

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