On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane

Wojciech Młocek; Marek Ptak

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 421-434
  • ISSN: 0011-4642

Abstract

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The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L 1 spaces.

How to cite

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Młocek, Wojciech, and Ptak, Marek. "On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane." Czechoslovak Mathematical Journal 63.2 (2013): 421-434. <http://eudml.org/doc/260671>.

@article{Młocek2013,
abstract = {The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between $L^\infty $ spaces on the unit circle and the real line we redefine the classical isomorphism between $L^1$ spaces.},
author = {Młocek, Wojciech, Ptak, Marek},
journal = {Czechoslovak Mathematical Journal},
keywords = {reflexive subspace; transitive subspace; Toeplitz operator; Hardy space; upper half-plane; reflexive subspace; transitive subspace; Toeplitz operator; Hardy space; upper half-plane},
language = {eng},
number = {2},
pages = {421-434},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane},
url = {http://eudml.org/doc/260671},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Młocek, Wojciech
AU - Ptak, Marek
TI - On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 421
EP - 434
AB - The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between $L^\infty $ spaces on the unit circle and the real line we redefine the classical isomorphism between $L^1$ spaces.
LA - eng
KW - reflexive subspace; transitive subspace; Toeplitz operator; Hardy space; upper half-plane; reflexive subspace; transitive subspace; Toeplitz operator; Hardy space; upper half-plane
UR - http://eudml.org/doc/260671
ER -

References

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  7. Duren, P. L., Theory of H p Spaces, Pure and Applied Mathematics, 38. Academic Press, New York-London (1970). (1970) MR0268655
  8. Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall Series in Modern Analysis, Englewood Cliffs, N.J., Prentice-Hall (1962). (1962) Zbl0117.34001MR0133008
  9. Koosis, P., Introduction to H p Spaces, London Mathematical Society Lecture Note Series. 40. Cambridge University Press, Cambridge (1980). (1980) Zbl0435.30001MR0565451
  10. Nikolski, N. K., Operators, Functions, and Systems: An Easy Reading. Volume I: Hardy, Hankel, and Toeplitz. Transl. from the French by Andreas Hartmann, Mathematical Surveys and Monographs, 92. American Mathematical Society, Providence (2002). (2002) Zbl1007.47001MR1864396
  11. Sarason, D., 10.2140/pjm.1966.17.511, Pac. J. Math. 17 (1966), 511-517. (1966) Zbl0171.33703MR0192365DOI10.2140/pjm.1966.17.511

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