In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.

This paper presents a patch-wise low-rank based image denoising method with constrained variational model involving local and nonlocal regularization. On one hand, recent patch-wise methods can be represented as a low-rank matrix approximation problem whose convex relaxation usually depends on nuclear norm minimization (NNM). Here, we extend the NNM to the nonconvex schatten p-norm minimization...

Sketching is a prominent algorithmic tool for processinglarge data. In this paper, we study the problem of sketchingmatrix norms. We consider two sketching models. The firstis bilinear sketching, in which there is a distribution overpairs of r×n matrices S and n× s matrices T such that forany fixed n×n matrix A, from S ·A ·T one can approximate‖A‖p up to an approxima...

in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators  are investigated.

We present numerical methods for computing the Schatten p-norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental design inverse problems, where defines a measure uncertainty. Computing high-dimensional matrices is computationally expensive. propose matrix-free method to estimate using Monte Carlo estimator derive convergence result...

The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related a conjecture an open question were presented by R. Lemos G. Soares in \cite{lemos}. In addition, we present complement unitarily invariant norm inequality was conjectured Bhatia, Y. Lim T. Yamazaki \cite{Bhatia2}, recently proved T.H. Dinh...

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...

Noisy data recovery is an important problem in machine learning field, which has widely applications for collaborative prediction, recommendation systems, etc. One popular model is to use trace norm model for noisy data recovery. However, it is ignored that the reconstructed data could be shrank (i.e., singular values could be greatly suppressed). In this paper, we present novel noisy data reco...