Abstract
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake the study of complex symmetric weighted composition operators, identifying several new classes of such operators.
Mathematics Subject Classification (2010). 47B33, 47B32, 47B99.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Paul S. Bourdon and Sivaram K. Narayan. Normal weighted composition operators on the Hardy space H2(U). J. Math. Anal. Appl., 367(1):278–286, 2010.
Paul S. Bourdon and Joel H. Shapiro. Riesz composition operators. Pacific J. Math., 181(2):231–246, 1997.
Nicolas Chevrot, Emmanuel Fricain, and Dan Timotin. The characteristic function of a complex symmetric contraction. Proc. Amer. Math. Soc., 135(9):2877–2886 (electronic), 2007.
Carl C. Cowen, Gajath Gunatillake, and Eungil Ko. Hermitian weighted composition operators and Bergman extremal functions. Complex Anal. Oper. Theory, 7(1):69– 99, 2013.
Carl C. Cowen and Eungil Ko. Hermitian weighted composition operators on H2. Trans. Amer. Math. Soc., 362(11):5771–5801, 2010.
Carl C. Cowen and Barbara D. MacCluer. Composition operators on spaces of analytic functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1995.
Stephan Ramon Garcia and Mihai Putinar. Complex symmetric operators and applications. Trans. Amer. Math. Soc., 358(3):1285–1315 (electronic), 2006.
Stephan Ramon Garcia and Mihai Putinar. Complex symmetric operators and applications. II. Trans. Amer. Math. Soc., 359(8):3913–3931 (electronic), 2007.
Stephan Ramon Garcia and Warren R. Wogen. Complex symmetric partial isometries. J. Funct. Anal., 257(4):1251–1260, 2009.
Stephan Ramon Garcia and Warren R. Wogen. Some new classes of complex symmetric operators. Trans. Amer. Math. Soc., 362(11):6065–6077, 2010.
T.M. Gilbreath and Warren R. Wogen. Remarks on the structure of complex symmetric operators. Integral Equations Operator Theory, 59(4):585–590, 2007.
Sungeun Jung, Eungil Ko, and Ji Eun Lee. On scalar extensions and spectral decompositions of complex symmetric operators. J. Math. Anal. Appl., 384(2):252–260, 2011.
S. Jung, E. Ko, M. Lee, and J. Lee. On local spectral properties of complex symmetric operators. J. Math. Anal. Appl., 379:325–333, 2011.
Chun Guang Li, Sen Zhu, and Ting Ting Zhou. Foguel operators with complex symmetry. Preprint.
S. Waleed Noor, Complex symmetry of composition operators induced by involutive ball automorphisms. Preprint.
Pietro Poggi-Corradini. The Hardy class of Koenigs maps. Michigan Math. J., 44(3):495–507, 1997.
Joel H. Shapiro. Composition operators and classical function theory. Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993.
James E. Tener. Unitary equivalence to a complex symmetric matrix: an algorithm. J. Math. Anal. Appl., 341(1):640–648, 2008.
**ao Huan Wang and Zong Sheng Gao. Some equivalence properties of complex symmetric operators. Math. Pract. Theory, 40(8):233–236, 2010.
Sergey M. Zagorodnyuk. On a J-polar decomposition of a bounded operator and matrix representations of J-symmetric, J-skew-symmetric operators. Banach J. Math. Anal., 4(2):11–36, 2010.
Sen Zhu, Chun Guang Li, and You Qing Ji. The class of complex symmetric operators is not norm closed. Proc. Amer. Math. Soc., 140(5):1705–1708, 2012.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Basel
About this paper
Cite this paper
Garcia, S.R., Hammond, C. (2014). Which Weighted Composition Operators are Complex Symmetric?. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes RodrĂguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0648-0_10
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0647-3
Online ISBN: 978-3-0348-0648-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)