We define positive Toeplitz operators between harmonic Bergman–Besov spaces $$b^p_\alpha $$ on the unit ball of $${\mathbb {R}}^n$$ for full ranges parameters $$0<p<\infty , $$\alpha \in {\mathbb {R}}$$ . give characterizations bounded and compact taking one space into another in terms Carleson vanishing measures. also a operator $$b^{2}_{\alpha }$$ to be Schatten class $$S_{p}$$ averaging func...

Let Sp be the Schatten-von Neumann ideal of compact operators equipped with the norm Np(·). For an A ∈ Sp (1 < p <∞), the inequality [ ∞ ∑ k=1 |Reλk(A)| ] 1 p + bp [ ∞ ∑ k=1 | Imλk(A)| ] 1 p ≥ Np(AR)− bpNp(AI) (bp = const. > 0) is derived, where λj(A) (j = 1, 2, . . . ) are the eigenvalues of A, AI = (A − A∗)/2i and AR = (A + A∗)/2. The suggested approach is based on some relations between the ...

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 address the problem of dynamic MRI reconstruction from partially sampled K-space data. Our work is motivated by previous studies in this area that proposed exploiting the spatiotemporal correlation of the dynamic MRI sequence by posing the reconstruction problem as a least squares minimization regularized by sparsity and low-rank penalties. Ideally the sparsity and low-rank pen...

Both sparse coding and rank minimization have led to great successes in various image processing tasks. Though the underlying principles of these two approaches are similar, no theory is available to demonstrate the correspondence. In this paper, starting by designing an adaptive dictionary for each group of image patches, we analyze the sparsity of image patches in each group using the rank mi...

Let A belong to the Schatten-von Neumann ideal Sp for 0 < p < ∞. We give an upper bound for the operator norm of the resolvent (zI − A)−1 of A in terms of the departure from normality of A and the distance of z to the spectrum of A. As an application we provide an upper bound for the Hausdorff distance of the spectra of two operators belonging to Sp.