The distribution function inequality for a finite sum of finite products of Toeplitz operators (original) (raw)

On Some Problems for Toeplitz and Truncated Toeplitz Operators

For a scalar inner function �, the model space of Sz.-Nagy and Foias is the subspace K� = H2 ⊖�H2 of the classical Hardy space H2 = H2(D) over the unit disk D = {z ∈ C : |z| < 1}. For a bounded linear operator A on the model space K�, its Berezin symbol is the function e A Kdefined on D by e A K�(�) = D

Binormal Toeplitz operators on the Hardy space

We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.

On Weighted Toeplitz Operators

2011

A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz operators are also determined.