in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function. However, most existing algorithms are too slow or even impractical for large-scale problems, due to the singular value decomposition (SVD) or eigenvalue decomposition (EVD) of the whole matrix in each iteration. In this paper, we rigorously prove that for any 0< p≤ 1, p1, p2 > 0 satisfying 1/p= 1/p...

It was shown in a previous work that some blind methods can be made robust to channel order overmodeling by using the l1 or lp quasi-norms. However, no theoretical argument has been provided to support this statement. In this work, we study the robustness of subspace blind based methods using l1 or lp quasi-norms. For the l1 norm, we provide the sufficient and necessary condition that the chann...

A posteriori error estimators based on quasi-norm gradient recovery are established for the finite element approximation of the p-Laplacian on unstructured meshes. The new a posteriori error estimators provide both upper and lower bounds in the quasi-norm for the discretization error. The main tools for the proofs of reliability are approximation error estimates for a local approximation operat...

The Schatten-p quasi-norm (0<p<1) is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schattenp quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we fi...

We address some theoretical guarantees for Schatten-p quasi-norm minimization (p ∈ (0, 1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measuring operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaran...

For Banach spaces X and Y, a bounded linear operator T:X⟶Y⁎ is said to weak-star quasi attains its norm if the σ(Y⁎,Y)-closure of image by T unit ball intersects sphere radius ‖T‖ centered at origin in Y⁎. This notion inspired quasi-norm attainment operators introduced studied [5]. As main result, we prove that set attaining dense space regardless choice spaces, furthermore, approximating can b...