We correct a formula of Gavish and Donoho for singular value shrinkage with operator norm loss non-square matrices. also observe that in the classical regime, optimal any Schatten converges to best linear predictor.

Not much has been known about these spaces except for some special cases. It was known since 1953 that every operator A ∈ B(H) is the sum of two commutators of bounded linear operators [35], [16] while the commutator spaces of Schatten ideals Lp , p > 0, were the subject of several studies over the last 30 years, notably [49], [66], [3], [68], [67], [4], [38] and [18]. Aside from these efforts,...

We characterize the 1-unconditional subsets (erc)(r,c)∈I of the set of elementary matrices in the Schatten-von-Neumann class S. The set of couples I must be the set of edges of a bipartite graph without cycles of even length 4 6 l 6 p if p is an even integer, and without cycles at all if p is a positive real number that is not an even integer. In the latter case, I is even a Varopoulos set of V...

In this paper, we focus on the weighted Bergman spaces Aφp in D with φ∈W0. We first give characterizations of those finite positive Borel measures µ such that embedding Aφp⊂Lμq is bounded or compact for 0<p,q<∞. Then describe Toeplitz operators Tμ from one space to another Aφq all possible Finally, characterize Schatten class Aφ2.

Let M (ω) be the modulation space with parameters p, q and weight function ω. We prove that if p1 = p2, q1 = q2, ω1 = ω0ω and ω2 = ω0, and ∂ a/ω0 ∈ L ∞ for all α, then the Ψdo at(x,D) : M p1,q1 (ω1) → M22 (ω2) is continuous. If instead a ∈ M p,q (ω) for appropriate p, q and ω, then we prove that the map here above is continuous, and if in addition pj = qj = 2, then we prove that at(x,D) is a Sc...

The paper contains three results, the common feature of which is that they deal with the Schatten p class. The first is a presentation of a new complemented subspace of Cp in the reflexive range (and p ̸= 2). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of Cp in C n p with small n and shows...