Essential Norm of Toeplitz Operators on the Fock Spaces

Abstract

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.

Toeplitz Operators with Positive Measures on Harmonic Fock Spaces

“…In 2010 §Isralowitz and Zhu discussed the boundedness, compactness and S p -class of Toeplitz operators T µ on Fock space F 2 α in [9]. Besides, during 2011-2015, Hu and Lv studied many properties of Toeplitz operators on [10,11,12].…”