TY  - JOUR
ID  - Câmara2024
LB  - Câmara2024
AU  - Câmara, M. Cristina
AU  - Kliś-Garlicka, Kamila
AU  - Ptak, Marek
TI  - Shifted model spaces and their orthogonal decompositions
ST  - Shifted model spaces and their orthogonal decompositions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 3
SP  - 341
EP  - 357
DO  - https://doi.org/10.7494/OpMath.2024.44.3.341
UR  - https://doi.org/10.7494/OpMath.2024.44.3.341
AB  - 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.
KW  - model space
KW  - Toeplitz operator
KW  - Toeplitz kernel
KW  - truncated Toeplitz operator
KW  - nearly invariant
KW  - shift invariant
SN  - 1232-9274
ER  -