Product of weighted Hankel and weighted Toeplitz operators

Demonstratio mathematica

article

Gopal Datt¹  Deepak Kumar Porwal¹ 

[1] Department of Mathematics, Pgdav College, University of Delhi

关键词: Toeplitz operator;    Hankel operator;    weighted Hankel operator;    weighted Toeplitz operator;   

DOI  :  10.1515/dema-2013-0467

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this paper, we discuss some properties of the weighted Hankel operator Hψβ$H_\psi ^\beta $ and describe the conditions on which the weighted Hankel operator Hψβ$H_\psi ^\beta $ and weighted Toeplitz operator Tϕβ$T_\phi ^\beta $, with ϕ , ψ ∈ L ∞ ( β ) on the space H 2 ( β ), β = { β n } n∈Ƶ being a sequence of positive numbers with β 0 = 1, commute. It is also proved that if a non-zero weighted Hankel operator Hψβ$H_\psi ^\beta $ commutes with Tϕβ$T_\phi ^\beta $, which is not a multiple of the identity, then Hψβ=μTϕβ$H_\psi ^\beta = \mu T_\phi ^\beta $, for some μ ∈ ℂ.

【 授权许可】

CC BY