On complex symmetric Toeplitz operators

Toeplitz Operators and Solvable C*-algebras on Hermitian Symmetric Spaces

Bounded symmetric domains (Cartan domains and exceptional domains) are higher-dimensional generalizations of the open unit disc. In this note we give a structure theory for the C*-algebra T generated by all Toeplitz operators Tf(h) := P{fh) with continuous symbol function ƒ G C(S) on the Shilov boundary 5 of a bounded symmetric domain D of arbitrary rank r. Here h belongs to the Hardy space H(S...

Index Theory for Toeplitz Operators on Bounded Symmetric Domains

In this note we give an index theory for Toeplitz operators on the Hardy space of the Shilov boundary of an arbitrary bounded symmetric domain. Our results generalize earlier work of Gohberg-Krein and Venugopalkrishna [12] for domains of rank 1 and of Berger-Coburn-Koranyi [1] for domains of rank 2. Bounded symmetric domains (Cartan domains, classical or exceptional) are the natural higher-dime...

On Weighted Toeplitz Operators

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 ope...

Complex Symmetric Operators and Applications

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, selfadjoint extensions of s...

Toeplitz Operators on Fock Spaces