Truncated Toeplitz operators and complex symmetries
HTML articles powered by AMS MathViewer
- by Hari Bercovici and Dan Timotin PDF
- Proc. Amer. Math. Soc. 146 (2018), 261-266 Request permission
Abstract:
We show that truncated Toeplitz operators are characterized by a collection of complex symmetries. This was conjectured by Kliś-Garlicka, Lanucha, and Ptak, and proved by them in some special cases.References
- Hari Bercovici, Operator theory and arithmetic in $H^\infty$, Mathematical Surveys and Monographs, vol. 26, American Mathematical Society, Providence, RI, 1988. MR 954383, DOI 10.1090/surv/026
- Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, and Warren R. Wogen, Truncated Toeplitz operators: spatial isomorphism, unitary equivalence, and similarity, Indiana Univ. Math. J. 59 (2010), no. 2, 595–620. MR 2648079, DOI 10.1512/iumj.2010.59.4097
- Joseph A. Cima, William T. Ross, and Warren R. Wogen, Truncated Toeplitz operators on finite dimensional spaces, Oper. Matrices 2 (2008), no. 3, 357–369. MR 2440673, DOI 10.7153/oam-02-21
- Stephan Ramon Garcia and Mihai Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358 (2006), no. 3, 1285–1315. MR 2187654, DOI 10.1090/S0002-9947-05-03742-6
- Stephan Ramon Garcia and William T. Ross, Recent progress on truncated Toeplitz operators, Blaschke products and their applications, Fields Inst. Commun., vol. 65, Springer, New York, 2013, pp. 275–319. MR 3052299, DOI 10.1007/978-1-4614-5341-3_{1}5
- Kamila Kliś-Garlicka, Bartosz Łanucha, and Marek Ptak, Characterization of truncated Toeplitz operators by conjugations, Oper. Matrices 11 (2017), no. 3, 807–822. MR 3655687, DOI 10.7153/oam-11-57
- Donald Sarason, Algebraic properties of truncated Toeplitz operators, Oper. Matrices 1 (2007), no. 4, 491–526. MR 2363975, DOI 10.7153/oam-01-29
Additional Information
- Hari Bercovici
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 34985
- Email: bercovic@indiana.edu
- Dan Timotin
- Affiliation: Simion Stoilow Institute of Mathematics, Romanian Academy, Calea Griviţei 21, Bucharest, Romania
- Email: dan.timotin@imar.ro
- Received by editor(s): February 3, 2017
- Received by editor(s) in revised form: February 27, 2017
- Published electronically: July 20, 2017
- Additional Notes: The first author was supported in part by a grant of the National Science Foundation.
- Communicated by: Stephan Ramon García
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 261-266
- MSC (2010): Primary 47A45; Secondary 47B32, 47B35
- DOI: https://doi.org/10.1090/proc/13717
- MathSciNet review: 3723138