Banach Journal of Mathematical Analysis

Skew symmetry of a class of operators

Chun Guang Li and Ting Ting Zhou

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Abstract

An operator $T$ on a complex Hilbert space $\mathcal{H}$ is said to be skew symmetric if there exists a conjugate-linear, isometric involution $C:\mathcal{H}\rightarrow\mathcal{H}$ such that $CTC=-T^*$. In this paper, using an interpolation theorem related to conjugations, we give a geometric characterization for a class of operators to be skew symmetric. As an application, we get a description of skew symmetric partial isometries.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 1 (2014), 279-294.

Dates
First available in Project Euclid: 14 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1381782100

Digital Object Identifier
doi:10.15352/bjma/1381782100

Mathematical Reviews number (MathSciNet)
MR3161695

Zentralblatt MATH identifier
1295.47014

Subjects
Primary: 47B25: Symmetric and selfadjoint operators (unbounded)
Secondary: 47A65: Structure theory

Keywords
skew symmetric operator complex symmetric operator compact operator partial isometry

Citation

Li, Chun Guang; Zhou, Ting Ting. Skew symmetry of a class of operators. Banach J. Math. Anal. 8 (2014), no. 1, 279--294. doi:10.15352/bjma/1381782100. https://projecteuclid.org/euclid.bjma/1381782100


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