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July 2019 The polar decomposition for adjointable operators on Hilbert C-modules and n-centered operators
Na Liu, Wei Luo, Qingxiang Xu
Banach J. Math. Anal. 13(3): 627-646 (July 2019). DOI: 10.1215/17358787-2018-0027

Abstract

Let n be any natural number. The n-centered operator is introduced for adjointable operators on Hilbert C-modules. Based on the characterizations of the polar decomposition for the product of two adjointable operators, n-centered operators, centered operators as well as binormal operators are clarified, and some results known for the Hilbert space operators are improved. It is proved that for an adjointable operator T, if T is Moore–Penrose invertible and is n-centered, then its Moore–Penrose inverse is also n-centered. A Hilbert space operator T is constructed such that T is n-centered, whereas it fails to be (n+1)-centered.

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Na Liu. Wei Luo. Qingxiang Xu. "The polar decomposition for adjointable operators on Hilbert C-modules and n-centered operators." Banach J. Math. Anal. 13 (3) 627 - 646, July 2019. https://doi.org/10.1215/17358787-2018-0027

Information

Received: 7 July 2018; Accepted: 28 August 2018; Published: July 2019
First available in Project Euclid: 25 May 2019

zbMATH: 07083765
MathSciNet: MR3978941
Digital Object Identifier: 10.1215/17358787-2018-0027

Subjects:
Primary: 46L08
Secondary: 47A05

Keywords: binormal operator , ‎centered operator , Hilbert $C^{*}$-module , n-centered operator , polar decomposition

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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