Normality of adjointable module maps

Abstract

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 $T^{\ast }$ such that $T=\mathcal{U}{T}^{\ast }.$ Kaplansky's theorem for normality of the product of bounded operators is also reformulated in the framework of Hilbert C*-modules.

8 pages / corrected typos, references updated

References in corpus (4)

• Adjointability of densely defined closed operators and the Magajna-Schweizer Theorem
• Generalized inverses and polar decomposition of unbounded regular operators on Hilbert $C^{\ast }$-modules
• The functional calculus for regular operators in Hilbert C*-modules revisited
• The gap between unbounded regular operators

Cited by in corpus (1)

• EP modular operators and their products