Additive commutators of operators belonging to two{sided ideals of B(H) are studied. J){commutators is characterized and found to equal IJ ; B(H)]. It is shown that three commutators are enough in I; B(H)], and that four are enough in I; J ]. Finally, some results about single commutators are proved, for example that every element of the Schatten class C p is a single (C p ; B(H)){commutator if...

It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomor-phic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative L p (N;)-spaces deened by a semi-nite, normal, faithful trace on a von Neumann algebra N. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting.

Low-rank tensor estimation has been frequently applied in many real-world problems. Despite successful applications, existing Schatten 1-norm minimization (SNM) methods may become very slow or even not applicable for large-scale problems. To address this difficulty, we therefore propose an efficient and scalable core tensor Schatten 1-norm minimization method for simultaneous tensor decompositi...

We study the boundedness and compactness of generalized Volterra integral operator on weighted Bergman spaces with doubling weights unit disc. A Toeplitz is defined boundedness, Schatten class membership this are investigated Hilbert space. As an application, operators also characterized. Finally, we get characterizations Hardy space $$H^2$$ .

We show convergence of the weak dual greedy algorithm in wide class of Banach spaces, extending our previous result where it was shown to converge in subspaces of quotients of Lp (for 1 < p < ∞). In particular, we show it converges in the Schatten ideals Sp when 1 < p < ∞ and in any Banach lattice which is p-convex and q-concave with constants one, where 1 < p < q < ∞. We also discuss convergen...

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group Γ and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum Λ ⊆ Γ , the norm of the Hilbert transform and th...

We prove the orthogonality (in the sense of Birkhoff) of the range and the kernel of an important class of elementary operators with respect to the Schatten p-class. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) b...

In this paper, we investigate singular integral operators induced by the Bergman kernel and Szegö on irreducible bounded symmetric domain in its standard Harish-Chandra realization. We completely characterize when Bergman-type Szegö-type belong to Schatten class operator ideals several analytic numerical invariants of domain. These results not only generalize a recent result Hilbert unit ball d...