Geodesic
On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 421-434
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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^\infty $ spaces on the unit circle and the real line we redefine the classical isomorphism between $L^1$ spaces.
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.
DOI : 10.1007/s10587-013-0026-0
Classification : 47B35, 47L05, 47L45, 47L80
Keywords: reflexive subspace; transitive subspace; Toeplitz operator; Hardy space; upper half-plane 
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Młocek, Wojciech; Ptak, Marek. On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 421-434. doi: 10.1007/s10587-013-0026-0

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