Annals of Functional Analysis

On Weyl completions of partial operator matrices

Xiufeng Wu, Junjie Huang, and Alatancang Chen

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Abstract

Let H and K be complex separable Hilbert spaces. Given the operators AB(H) and BB(K,H), we define MX,Y:=[ABXY], where XB(H,K) and YB(K) are unknown elements. In this article, we give a necessary and sufficient condition for MX,Y to be a (right) Weyl operator for some XB(H,K) and YB(K). Moreover, we show that if dimK<, then MX,Y is a left Weyl operator for some XB(H,K) and YB(K) if and only if [AB] is a left Fredholm operator and ind([AB])dimK; if dimK=, then MX,Y is a left Weyl operator for some XB(H,K) and YB(K).

Article information

Source
Ann. Funct. Anal., Volume 10, Number 2 (2019), 229-241.

Dates
Received: 9 May 2018
Accepted: 17 July 2018
First available in Project Euclid: 19 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.afa/1552960865

Digital Object Identifier
doi:10.1215/20088752-2018-0018

Mathematical Reviews number (MathSciNet)
MR3941384

Zentralblatt MATH identifier
07083891

Subjects
Primary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]
Secondary: 47B99: None of the above, but in this section 47A10: Spectrum, resolvent

Keywords
right (left) Weyl operator Weyl operator partial operator matrices completion problem

Citation

Wu, Xiufeng; Huang, Junjie; Chen, Alatancang. On Weyl completions of partial operator matrices. Ann. Funct. Anal. 10 (2019), no. 2, 229--241. doi:10.1215/20088752-2018-0018. https://projecteuclid.org/euclid.afa/1552960865


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