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Spectral and polar decomposition in AW*-algebras

Michael Frank
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Abstract

We show the possibility and the uniqueness of polar decomposition of elements of arbitrary AW*-algebras inside them. We prove that spectral decomposition of normal elements of normal AW*-algebras is possible and unique inside them. The possibility of spectral decomposition of normal elements does not depend on the normality of the AW*-algebra under consideration.

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Michael Frank. 1993-03-11. Spectral and polar decomposition in AW*-algebras. https://arxiv.org/abs/funct-an/9303001

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