Symbols of compact truncated Toeplitz operators

2021/07/19 by O'Loughlin, Ryan
#30H10 #46E20 #47B35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2107.09115

Abstract

This paper characterises the dual of the model space K_I¹, where I is an inner function, intersected with the shifted Hardy space, z H¹. With this duality result, it is then shown that every bounded truncated Toeplitz operator on the model space K_I² has a bounded symbol if and only if every compact truncated Toeplitz operator on K_I² has a symbol which is of the form I multiplied by a continuous function.

Related

• Recent results on truncated Toeplitz operators
• Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators
• Schatten-class Truncated Toeplitz Operators
• Product of truncated Hankel and truncated Toeplitz operators
• Algebras of truncated Toeplitz operators