Intertwining analytic Toeplitz operators.

Intertwining Relations and Extended Eigenvalues for Analytic Toeplitz Operators

We study the intertwining relation XTφ = TψX where Tφ and Tψ are the Toeplitz operators induced on the Hardy space H 2 by analytic functions φ and ψ, bounded on the open unit disc U, and X is a nonzero bounded linear operator on H. Our work centers on the connection between intertwining and the image containment ψ(U) ⊂ φ(U), as well as on the nature of the intertwining operator X. We use our re...

On the analytic properties of intertwining operators I‎: ‎global normalizing factors

‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

Which subnormal Toeplitz operators are either normal or analytic ?

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos’s Problem 5: Which subnormal block Toeplitz operators are either normal or analytic ? We extend and prove Abrahamse’s Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol ...

Intertwining Operators and Residues

Toeplitz Operators

This article discusses Paul Halmos’s crucial work on Toeplitz operators and the consequences of that work. Mathematics Subject Classification (2000). 47B35.