We study time-frequency localization operators of the form A12 a , where a is the symbol of the operator and φ1, φ2 are the analysis and synthesis windows, respectively. It is shown in [3] that a sufficient condition for A12 a ∈ Sp(L(R)), the Schatten class of order p, is that a belongs to the modulation space Mp,∞(R2d) and the window functions to the modulation space M1. Here we prove a partia...

For a positive integer n, let Mn be the set of n × n complex matrices. Suppose ‖ · ‖ is the Ky Fan k-norm with 1 ≤ k ≤ mn or the Schatten p-norm with 1 ≤ p ≤ ∞ (p 6= 2) on Mmn, where m,n ≥ 2 are positive integers. It is shown that a linear map φ : Mmn →Mmn satisfying ‖A⊗B‖ = ‖φ(A⊗B)‖ for all A ∈Mm and B ∈Mn if and only if there are unitary U, V ∈ Mmn such that φ has the form A ⊗ B 7→ U(φ1(A) ⊗ ...

Let ii be a bounded symmetric domain in C with normalized 2 volume measure dV . Let P be the orthogonal projection from L (il, dV) 2 2 onto the Bergman space La(Q) of holomorphic functions in L (ii, dV). Let P be the orthogonal projection from L (ii, dV) onto the closed subspace of antiholomorphic functions in L (ii, dV). The "little" Hankel operator h, with symbol / is the operator from La(Ci)...

We show that many invariant subspaces M for d-shifts (S1, . . . , Sd) of finite rank have the property that the orthogonal projection PM onto M satisfies PMSk − SkPM ∈ L, 1 ≤ k ≤ d for every p > 2d, L denoting the Schatten-von Neumann class of all compact operators having p-summable singular value lists. In such cases, the d tuple of operators T̄ = (T1, . . . , Td) obtained by compressing (S1, ....

For α, β > 0 and for a locally integrable function (or, more generally , a distribution) ϕ on (0, ∞), we study integral ooperators G α,β ϕ on L 2 (R +) defined by G α,β ϕ f (x) = R+ ϕ x α + y β f (y)dy. We describe the bounded and compact operators G α,β ϕ and operators G α,β ϕ of Schatten–von Neumann class S p. We also study continuity properties of the averaging projection Q α,β onto the oper...