Shifted model spaces and their orthogonal decompositions

• Autorzy: Câmara M. Cristina , Kliś-Garlicka Kamila , Ptak Marek

Identyfikatory

DOI

10.7494/OpMath.2024.44.3.341

• Języki publikacji: EN

Abstrakty

EN

We generalize certain well known orthogonal decompositions of model spaces and obtain similar decompositions for the wider class of shifted model spaces, allowing us to establish conditions for near invariance of the latter with respect to certain operators which include, as a particular case, the backward shift S*. In doing so, we illustrate the usefulness of obtaining appropriate decompositions and, in connection with this, we prove some results on model spaces which are of independent interest. We show moreover how the invariance properties of the kernel of an operator T, with respect to another operator, follow from certain commutation relations between the two operators involved.

Słowa kluczowe

EN

model space; Toeplitz operator; Toeplitz kernel; truncated Toeplitz operator; nearly invariant; shift invariant

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2024
• Tom: Vol. 44, no. 3
• Strony: 341--357
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Câmara M. Cristina

• Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

• https://orcid.org/0000-0001-9015-3980

autor

Kliś-Garlicka Kamila

• Department of Applied Mathematics, University of Agriculture, ul. Balicka 253c, 30-198 Kraków, Poland

• https://orcid.org/0000-0002-7104-1729

autor

Ptak Marek

• Department of Applied Mathematics, University of Agriculture, ul. Balicka 253c, 30-198 Kraków, Poland

• https://orcid.org/0000-0002-3843-7932

Bibliografia

• [1] I. Chalendar, E. Gallardo-Gutiérrez, J.R. Partington, A Beurling theorem for almost-invariant subspaces of the shift operator, J. Operator Theory 83 (2020), 321–331.
• [2] M.C. Câmara, J.R. Partington, Near invariance and kernels of Toeplitz operators, J. Anal. Math. 124 (2014), 235–260.
• [3] M.C. Câmara, J.R. Partington, Asymmetric truncated Toeplitz operators and Toeplitz operators with matrix symbol, J. Oper. Theory 77 (2017), 455–479.
• [4] M.C. Câmara, M.T. Malheiro, J.R. Partington, Model spaces and Toeplitz kernels in reflexive Hardy spaces, Oper. Matrices 10 (2016), 127–148.
• [5] M.C. Câmara, K. Kliś-Garlicka, M. Ptak, General Toeplitz kernels and pX, Y q-invariance, Canadian J. Math. (2023), 1–27.
• [6] E. Fricain, A. Hartmann, W.T. Ross, Range spaces of co-analytic Toeplitz operators, Canad. J. Math. 70 (2018), no. 6, 1261–1283.
• [7] S.R. Garcia, J.E. Mashreghi, W. Ross, Introduction to Model Spaces and their Operators, Cambridge Studies in Advanced Mathematics, vol. 148, Cambridge University Press, 2016.
• [8] A. Hartmann, W.T. Ross, Truncated Toeplitz operators and boundary values in nearly invariant subspaces, Complex Anal. Oper. Theory 7 (2013), no. 1, 261–273.
• [9] E. Hayashi, The kernel of a Toeplitz operators, Integral Equations Operator Theory 9 (1986), 587–591.
• [10] D. Hitt, Invariant subspaces of H2 of an annulus, Pacific J. Math. 134 (1988), 101–120.
• [11] N.K. Nikolskii, Treatise on the Shift Operator, Springer-Verlag, Berlin, Heidelberg, 1986.
• [12] R. O’Loughlin, Nearly invariant subspaces with applications to truncated Toeplitz operators, Complex Anal. Oper. Theory 14 (2020), Article no. 86.
• [13] D. Sarason, Nearly invariant subspaces of the backward shift, Contributions to Operator Theory and its Applications, Operator Theory: Advances and Applications 35 (1988), 481–493.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)