Multipliers and equivalence of functions, spaces, and operators

2023/07/11 by Camara, Cristina, Ross, Carlos Carteiro. William T.
#30D55 #30J05 #47A15 #47A65 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.05453

Abstract

This paper offers a unified approach to determining when two generalized Toeplitz operators on L² are equivalent. This will be done through multipliers between closed subspaces of L². Our discussion will include Toeplitz operators (and their duals) on the Hardy space, Hankel operators, asymmetric truncated Toeplitz operators, and dual asymmetric truncated Toeplitz operators. Along the way, there will be a discussion of equivalence of functions and kernels of generalized Toeplitz operators and a generalization of the Brown--Halmos theorem for this class of operators.

Related

• Multiplier Between Generalized Toeplitz Kernels
• Invertibility Issues for Toeplitz plus Hankel Operators and Their Close Relatives
• Hankel and Toeplitz operators: continuous and discrete representations
• Multipliers and equivalences between Toeplitz kernels
• Toeplitz and Hankel operators between distinct Hardy spaces