The Brown-Halmos theorem for a pair of abstract Hardy spaces

2018/02/23 by Karlovich, Alexei, Shargorodsky, Eugene
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1802.08438

Abstract

Let H[X] and H[Y] be abstract Hardy spaces built upon Banach function spaces X and Y over the unit circle \mathbbT. We prove an analogue of the Brown-Halmos theorem for Toeplitz operators T_a acting from H[X] to H[Y] under the only assumption that the space X is separable and the Riesz projection P is bounded on the space Y. We specify our results to the case of variable Lebesgue spaces X=L^p(⋅) and Y=L^q(⋅) and to the case of Lorentz spaces X=Y=L^p,q(w), 1

Related

• Toeplitz and Hankel operators between distinct Hardy spaces
• On the essential norms of Toeplitz operators on abstract Hardy spaces built upon Banach function spaces
• Brown Halmos Operator Identity and Toeplitz Operators on the Dirichlet Space
• Paired operators and paired kernels
• Brown-Halmos type characterization for the tetrablock