Toeplitz kernels and model spaces

2017/11/13 by Câmara, M. Cristina, Partington, Jonathan R.
#30H10 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1711.04511

Abstract

We review some classical and more recent results concerning kernels of Toeplitz operators and their relations with model spaces, which are themselves Toeplitz kernels of a special kind. We highlight the fundamental role played by the existence of maximal vectors for every nontrivial Toeplitz kernel.

Related

• Multipliers and equivalences between Toeplitz kernels
• Maximal functions, conjugations and multipliers between Toeplitz kernels
• Model spaces and Toeplitz kernels in reflexive Hardy spaces
• Composition operators between Toeplitz kernels
• Kernels of Toeplitz operators