Normal and cohyponormal weighted composition operators on H2

Carl C. Cowen; Sungeun Jung; Eungil Ko

doi:10.1007/978-3-319-06266-2_4

Normal and cohyponormal weighted composition operators on H²

Carl C. Cowen, Sungeun Jung, Eungil Ko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

In this paper we study normal and cohyponormal weighted composition operators on the Hardy space H². We show that if W_f,ᵠ is cohyponormal, then f is outer and ϕ is univalent. Moreover, we prove that when the composition map ᵠ has the Denjoy-Wolff point in the open unit disk, W_f,ᵠ is cohyponormal if and only if it is normal; in this case, f and ᵠ can be expressed as linear fractional maps. As a corollary, we find the polar decomposition of the cohyponormal operator W_f,ᵠ. Finally, we examine the commutant of a cohyponormal weighted composition operator.

Original language	English
Pages (from-to)	69-85
Number of pages	17
Journal	Operator Theory: Advances and Applications
Volume	240
DOIs	https://doi.org/10.1007/978-3-319-06266-2_4
State	Published - 2014

Bibliographical note

Publisher Copyright:
© 2014 Springer International Publishing Switzerland.

Keywords

Cohyponormal operator
Commutant
Composition operator
Hyponormal operator
Inner-outer factorization
Normal operator
Polar decomposition
Weighted composition operator

Access to Document

10.1007/978-3-319-06266-2_4

Cite this

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abstract = "In this paper we study normal and cohyponormal weighted composition operators on the Hardy space H2. We show that if Wf,ᵠ is cohyponormal, then f is outer and ϕ is univalent. Moreover, we prove that when the composition map ᵠ has the Denjoy-Wolff point in the open unit disk, Wf,ᵠ is cohyponormal if and only if it is normal; in this case, f and ᵠ can be expressed as linear fractional maps. As a corollary, we find the polar decomposition of the cohyponormal operator Wf,ᵠ. Finally, we examine the commutant of a cohyponormal weighted composition operator.",

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T1 - Normal and cohyponormal weighted composition operators on H2

AU - Cowen, Carl C.

AU - Jung, Sungeun

AU - Ko, Eungil

PY - 2014

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N2 - In this paper we study normal and cohyponormal weighted composition operators on the Hardy space H2. We show that if Wf,ᵠ is cohyponormal, then f is outer and ϕ is univalent. Moreover, we prove that when the composition map ᵠ has the Denjoy-Wolff point in the open unit disk, Wf,ᵠ is cohyponormal if and only if it is normal; in this case, f and ᵠ can be expressed as linear fractional maps. As a corollary, we find the polar decomposition of the cohyponormal operator Wf,ᵠ. Finally, we examine the commutant of a cohyponormal weighted composition operator.

AB - In this paper we study normal and cohyponormal weighted composition operators on the Hardy space H2. We show that if Wf,ᵠ is cohyponormal, then f is outer and ϕ is univalent. Moreover, we prove that when the composition map ᵠ has the Denjoy-Wolff point in the open unit disk, Wf,ᵠ is cohyponormal if and only if it is normal; in this case, f and ᵠ can be expressed as linear fractional maps. As a corollary, we find the polar decomposition of the cohyponormal operator Wf,ᵠ. Finally, we examine the commutant of a cohyponormal weighted composition operator.

KW - Cohyponormal operator

KW - Commutant

KW - Composition operator

KW - Hyponormal operator

KW - Inner-outer factorization

KW - Normal operator

KW - Polar decomposition

KW - Weighted composition operator

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