Truncated Toeplitz operators of finite rank
HTML articles powered by AMS MathViewer
- by R. V. Bessonov PDF
- Proc. Amer. Math. Soc. 142 (2014), 1301-1313 Request permission
Abstract:
We give a complete description of the finite-rank truncated Toeplitz operators.References
- Donald Sarason, Algebraic properties of truncated Toeplitz operators, Oper. Matrices 1 (2007), no. 4, 491–526. MR 2363975, DOI 10.7153/oam-01-29
- P. R. Ahern and D. N. Clark, Radial limits and invariant subspaces, Amer. J. Math. 92 (1970), 332–342. MR 262511, DOI 10.2307/2373326
- Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89–102. MR 160136, DOI 10.1007/978-1-4613-8208-9_{1}9
- Anton Baranov, Roman Bessonov, and Vladimir Kapustin, Symbols of truncated Toeplitz operators, J. Funct. Anal. 261 (2011), no. 12, 3437–3456. MR 2838030, DOI 10.1016/j.jfa.2011.08.005
- N. K. Nikol′skiĭ, Treatise on the shift operator, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986. Spectral function theory; With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by Jaak Peetre. MR 827223, DOI 10.1007/978-3-642-70151-1
- Joseph A. Cima, Alec L. Matheson, and William T. Ross, The Cauchy transform, Mathematical Surveys and Monographs, vol. 125, American Mathematical Society, Providence, RI, 2006. MR 2215991, DOI 10.1090/surv/125
- 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 Mihai Putinar, Complex symmetric operators and applications. II, Trans. Amer. Math. Soc. 359 (2007), no. 8, 3913–3931. MR 2302518, DOI 10.1090/S0002-9947-07-04213-4
- Douglas N. Clark, One dimensional perturbations of restricted shifts, J. Analyse Math. 25 (1972), 169–191. MR 301534, DOI 10.1007/BF02790036
- A. G. Poltoratskiĭ, Boundary behavior of pseudocontinuable functions, Algebra i Analiz 5 (1993), no. 2, 189–210 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 5 (1994), no. 2, 389–406. MR 1223178
- Anton Baranov, Isabelle Chalendar, Emmanuel Fricain, Javad Mashreghi, and Dan Timotin, Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators, J. Funct. Anal. 259 (2010), no. 10, 2673–2701. MR 2679022, DOI 10.1016/j.jfa.2010.05.005
Additional Information
- R. V. Bessonov
- Affiliation: St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191023, Russia
- Address at time of publication: Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, St. Petersburg, 199178, Russia
- Email: bessonov@pdmi.ras.ru
- Received by editor(s): February 6, 2012
- Received by editor(s) in revised form: May 14, 2012
- Published electronically: January 28, 2014
- Additional Notes: This work was partially supported by RFBR grant 11-01-00584-a, by V. A. Rokhlin grant 2012, and by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026
- Communicated by: Richard Rochberg
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 1301-1313
- MSC (2010): Primary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-2014-11861-2
- MathSciNet review: 3162251