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.

We say that the quasi-norm Φ of a symmetric sequence space E has property P if, for all x, y ∈ E with 0 ≤ xn ≤ yn for all n, and xN < yN for some N , we have Φ (xn) < Φ (yn) . Simon [6] proved that if the Banach norm Φ has property P , then whenever An → A in the weak operator topology on the unitary matrix space CE and Φ(An)→ Φ(A), then An → A in the strong operator topology on CE . In this no...

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...

Following the book [9] by Dunkl and Xu and the paper [23] by Xu we will assume that αj ≥ 0 for each j = 0, 1, . . . , k although one would expect that the range of validity can be extended analytically to the domain αj > −12 for each j. We will also exclude the case k = 1, α0 = α1 = 0 because we want the constant μ defined below in (1.5) to be positive. The parity vector p = (p0, p1, . . . , pk...

&lt;p&gt;In this article, we introduce the concept of a soft quasi-pseudometric space. We show that every induces compatible on collection all points absolute set whenever parameter is finite. then Isbell convexity and self non-expansive map quasi-metric space has nonempty convex fixed point set.&lt;/p&gt;

where g:(0, 1)-»X is an essentially bounded strongly measurable function. In this paper we examine analogues of the Radon-Nikodym Property for quasiBanach spaces. If 0 < p < 1, there are several possible ways of defining "differentiable" operators on Lp, but they inevitably lead to the conclusion that the only differentiable operator is zero. For example, a differentiable operator on L\ has the...

This paper concerns itself with Besov space solutions of the 2-D quasi-geostrophic (QG) equation with dissipation induced by a fractional Laplacian (−1)α . The goal is threefold: first, to extend a previous result on solutions in the inhomogeneous Besov space Br 2,q [J. Wu, Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces, SIAM J. Math. Anal. 36 (2004–2005) 1014...

In cite{Kats84}, Katsaras introduced a method for constructing a Hu-tton $[0,1]$-quasi-uniformity from a crisp uniformity. In this paper we present other different methods for making this based mainly in the concept of a fuzzy uniform structure. Furthermore, we prove that some of these methods preserve the completeness property of the quasi-uniformity.  Moreover, we also show that Katsaras' con...