Hankel and Toeplitz: Sibling Operators on the Space H2

Abstract

Toeplitz matrices and operators, Toeplitz operators on l 2 (ℤ + ). The existence of the symbol, the discrete Hilbert transform. The Hankel matrices and operators: the existence of the symbol (Nehari), compact and finite rank Hankel operators. The Berezin transform, the Garsia norm, the spaces BMO, VMO, H ∞ + C and QC, the compact commutators.