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August 2019 Some spectra properties of unbounded 2×2 upper triangular operator matrices
Qingmei Bai, Alatancang Chen, Junjie Huang
Ann. Funct. Anal. 10(3): 412-424 (August 2019). DOI: 10.1215/20088752-2018-0039

Abstract

Let MC=[AC0B]:D(A)D(B)HKHK be a closed operator matrix acting in the Hilbert space HK. In this paper, we concern ourselves with the completion problems of MC. That is, we exactly describe the sets CCB+(K,H)σ(MC) and CCB+(K,H)σcr(MC), where σ(MC) includes the residual spectrum, the continuous spectrum, and the closed range spectrum of MC, and CB+(K,H) denotes the set of closable operators C:D(C)KH such that D(C)D(B) for a given closed operator B acting in K.

Citation

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Qingmei Bai. Alatancang Chen. Junjie Huang. "Some spectra properties of unbounded 2×2 upper triangular operator matrices." Ann. Funct. Anal. 10 (3) 412 - 424, August 2019. https://doi.org/10.1215/20088752-2018-0039

Information

Received: 16 November 2018; Accepted: 15 December 2018; Published: August 2019
First available in Project Euclid: 6 August 2019

zbMATH: 07089127
MathSciNet: MR3989185
Digital Object Identifier: 10.1215/20088752-2018-0039

Subjects:
Primary: 47A10
Secondary: 46C05

Keywords: closed range spectrum , continuous spectrum , maximal Tseng inverse , residual spectrum , upper triangular operator matrix

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 3 • August 2019
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