Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels

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Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels. / Harper, Zen; Smith, Martin P.

In: Journal of Operator Theory, Vol. 55, No. 2, 2006, p. 349-371.

Research output: Contribution to journalArticlepeer-review

Harvard

Harper, Z & Smith, MP 2006, 'Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels', Journal of Operator Theory, vol. 55, no. 2, pp. 349-371.

APA

Harper, Z., & Smith, M. P. (2006). Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels. Journal of Operator Theory, 55(2), 349-371.

Vancouver

Harper Z, Smith MP. Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels. Journal of Operator Theory. 2006;55(2):349-371.

Author

Harper, Zen ; Smith, Martin P. / Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels. In: Journal of Operator Theory. 2006 ; Vol. 55, No. 2. pp. 349-371.

Bibtex - Download

@article{3f0f5b22b5f640b0b5fc3f7389e3b695,
title = "Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels",
abstract = "Given an operator A on a Hilbert space H and c G H, we consider operators Lambda(A,c) defined on analytic functions f by Lambda(A,c)f = f (A)c. Special cases of Lambda(A,c) include vectorial Hankel operators, Carleson embeddings and weighted composition operators. For certain A, we determine conditions under which Lambda(A,c) extends to an operator of Schatten von-Neumann class on the Hardy or Bergman space of the disc. These conditions involve only the action of Lambda(A,c) on reproducing kernels and their derivatives. We also give corresponding results for operators on the Hardy space of the half-plane.",
keywords = "Schatten classes, reproducing kernels, Hardy space, Bergman space, Hankel operators, Carleson embeddings, composition operators, WEISS CONJECTURE",
author = "Zen Harper and Smith, {Martin P.}",
year = "2006",
language = "English",
volume = "55",
pages = "349--371",
journal = "Journal of Operator Theory",
issn = "1841-7744",
number = "2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Testing Schatten class Hankel operators, Carleson embeddings and weighted composition operators on reproducing kernels

AU - Harper, Zen

AU - Smith, Martin P.

PY - 2006

Y1 - 2006

N2 - Given an operator A on a Hilbert space H and c G H, we consider operators Lambda(A,c) defined on analytic functions f by Lambda(A,c)f = f (A)c. Special cases of Lambda(A,c) include vectorial Hankel operators, Carleson embeddings and weighted composition operators. For certain A, we determine conditions under which Lambda(A,c) extends to an operator of Schatten von-Neumann class on the Hardy or Bergman space of the disc. These conditions involve only the action of Lambda(A,c) on reproducing kernels and their derivatives. We also give corresponding results for operators on the Hardy space of the half-plane.

AB - Given an operator A on a Hilbert space H and c G H, we consider operators Lambda(A,c) defined on analytic functions f by Lambda(A,c)f = f (A)c. Special cases of Lambda(A,c) include vectorial Hankel operators, Carleson embeddings and weighted composition operators. For certain A, we determine conditions under which Lambda(A,c) extends to an operator of Schatten von-Neumann class on the Hardy or Bergman space of the disc. These conditions involve only the action of Lambda(A,c) on reproducing kernels and their derivatives. We also give corresponding results for operators on the Hardy space of the half-plane.

KW - Schatten classes

KW - reproducing kernels

KW - Hardy space

KW - Bergman space

KW - Hankel operators

KW - Carleson embeddings

KW - composition operators

KW - WEISS CONJECTURE

M3 - Article

VL - 55

SP - 349

EP - 371

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 1841-7744

IS - 2

ER -