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BanachJ.Math.Anal.8(2014),no.1,279–294 SKEWSYMMETRYOFACLASSOFOPERATORS B J M A

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Banach J. Math. Anal. 8 (2014), no. 1, 279–294

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anach

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ournal of

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athematical

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nalysis ISSN: 1735-8787 (electronic)

www.emis.de/journals/BJMA/

SKEW SYMMETRY OF A CLASS OF OPERATORS

CHUN GUANG LI1∗ AND TING TING ZHOU2 Communicated by M. Frank

Abstract. An operator T on a complex Hilbert spaceH is said to be skew symmetric if there exists a conjugate-linear, isometric involutionC : H → H such thatCT C =−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.

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P.R. China.

E-mail address: [email protected]

2 Institute of Mathematics, Jilin University, Changchun 130012, P.R. China.

E-mail address: [email protected]

Date: Received: 30 May 2013; Accepted: 13 June 2013.

∗ Corresponding author.

2010Mathematics Subject Classification. Primary 47B25; Secondary 47A65.

Key words and phrases. Skew symmetric operator, complex symmetric operator, compact operator, partial isometry.

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