Cartesian and polar decompositions of hyponormal operators
type: Item
instance of: scholarly article
title: Cartesian and polar decompositions of hyponormal operators
zbMATH Open document ID: 0538.47015
DOI: 10.1007/BF01161652
author: Peng Fan
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173555
review text: For the partially isometric part and the positive part in the polar decomposition of a hyponormal operator (on a complex separable Hilbert space), we obtain respectively: Theorem 1. The singular subspace of the (unique) partially isometric part of a hyponormal operator reduces the operator itself. Theorem 2. The positive part of a pure hyponormal operator can not possess eigenvalue of finite multiplicity at the maximum of its spectrum, but it can at the minimum. In addition, we obtain a new proof for a slightly refined version of a well known structure theorem concerning Cartesian decomposition of hyponormal operators. (The refined version reads as follows: The singular subspace of the real (imaginary) part of a hyponormal operator reduces the operator itself. In fact, it is this result and its proof that motivate the formulation and proof of Theorem 1.)
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 3855805
zbMATH Keywords: polar decomposition of a hyponormal operator
zbMATH Keywords: Cartesian decomposition of hyponormal operators
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3855805