Toeplitz Operators and Carleson Measures on Generalized Bargmann–Fock Spaces

Schuster, Alexander; Varolin, Dror

doi:10.1007/s00020-011-1939-3

Cited by 60 publications

(81 citation statements)

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“…And for the generalized Fock space F p (ϕ), the Fock-Carleson measure was characterized in [16]. It was proved there, a positive Borel measure μ is a Fock-Carleson measure if and only if…”

Section: Essential Norm Of Toeplitz Operators On Fock Spacesmentioning

confidence: 99%

“…Therefore, the Fock-Carleson measures are independent of the precise value of p. With this characterization, we can study positive Toeplitz operators T μ with positive measure symbols. The following Lemma 3.2 was first obtained in [9,16].…”

Section: Essential Norm Of Toeplitz Operators On Fock Spacesmentioning

confidence: 99%

“…The approach in the proof of Proposition 3.4 in [16] also works for this operator T . That is, for p ∈ [1, ∞] we have some constant C such that…”

Section: Lemma 34 If μ Is a Fock-carleson Measure There Is Some Comentioning

confidence: 99%

“…We define the generalized Fock space When dμ = gdv with some function g we write T g for T μ . More references on Toeplitz operators on Fock spaces, see [4,9,12,13,16].…”

Section: Introductionmentioning

confidence: 99%

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Essential Norm of Toeplitz Operators on the Fock Spaces

2015

Integr. Equ. Oper. Theory

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In this paper, we show that, on the generalized Fock space F p (ϕ) with 1 < p < ∞, the essential norm of a noncompact Toeplitz operator Tμ with |μ| being a Fock-Carleson measure equals its distance to the set of compact Toeplitz operators. Moreover, the distance is realized by infinitely many compact Toeplitz operators. Our approach is also available on the Bergman space setting.Mathematics Subject Classification. Primary 47B38; Secondary 32A36, 47G10.

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Section: Essential Norm Of Toeplitz Operators On Fock Spacesmentioning

confidence: 99%

Section: Essential Norm Of Toeplitz Operators On Fock Spacesmentioning

confidence: 99%

“…The approach in the proof of Proposition 3.4 in [16] also works for this operator T . That is, for p ∈ [1, ∞] we have some constant C such that…”

Section: Lemma 34 If μ Is a Fock-carleson Measure There Is Some Comentioning

confidence: 99%

“…We define the generalized Fock space When dμ = gdv with some function g we write T g for T μ . More references on Toeplitz operators on Fock spaces, see [4,9,12,13,16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations