Generalized Riesz projections and Toeplitz operators

Deviations of Riesz Projections of Hill Operators with Singular Potentials

Generalized Orthogonal Projections and Shorted Operators

Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and 〈 , 〉A : H×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉, ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = Q∗A} for different choi...

Weighted projections and Riesz frames

Let H be a (separable) Hilbert space and {ek}k≥1 a fixed orthonormal basis of H. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis. This is used to refine previous work on scaled projections, and to obtain a new characteri...

Toeplitz Operators and Localization Operators

We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator D such that the localization operator with symbol f coincides with the Toeplitz operator with symbol Df . An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Co...

Toeplitz Operators

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