In this paper we study four properties related to the existence of a dense metrizable subspace of a generalized ordered (GO) space. Three of the properties are classical, and one is recent. We give new characterizations of GO-spaces that have dense metrizable subspaces, investigate which GO-spaces can embed in GO spaces with one of the four properties, and provide examples showing the relations...

A space X is said to be κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable iff it is ∆(X)-resolvable, where ∆(X) = min{|G| : G 6= ∅ open}. We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ = mi...

The talk will present a reliable Krylov-subspace method for estimating the spectral condition number of a matrix A. The main difficulty in estimating the condition number is the estimation of the smallest singular value  min of A. Our method estimates this value by solving a consistent least-squares minimization problem with a known minimizer using a specific Krylov-subspace method called LSQR...

Clustering has been recognized as an important and valuable capability in the data mining field. Instead of finding clusters in the full feature space, subspace clustering is an emergent task which aims at detecting clusters embedded in subspaces. Most of previous works in the literature are density-based approaches, where a cluster is regarded as a high-density region in a subspace. However, t...

In this note, we provide a few sufficient conditions for the invariant subspace problem. Introduction An important open problem in operator theory is the invariant subspace problem. Since the problem is solved for all finite dimensional complex vector spaces of dimension at least 2, H denotes a separable Hilbert space whose dimension is infinite. It is enough to think for a contraction T , that...

We investigate the bifurcation mechanism for the loss of transverse stability of the chaotic attractor in an invariant subspace in an asymmetric dynamical system. It is found that a direct transition to global riddling occurs through a transcritical contact bifurcation between a periodic saddle embedded in the chaotic attractor on the invariant subspace and a repeller on its basin boundary. Thi...

Let X = {a}∪ {ai | i ∈ N} be a subspace of Euclidean space E such that limi→∞ ai = a and ai 6= aj for i 6= j. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y ) of all homeomorphisms on Y , where Y = {a, b} ∪ {...

We discuss some perturbation results concerning certain pairs of sequences vectors in a Hilbert space $\Hil$ and producing new which share, with the original ones, { reconstruction formulas on dense subspace or whole space}. also propose preliminary same issue, but distributional settings.

The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subse...

Often, we work with vector spaces which consists of an appropriate. Many concepts concerning vectors in Rn can be extended to other mathematical systems. We can think of a vector space in.of a finite-dimensional nontrivial proper subspace of such a vector space is equivalent to ACA0 over RCA0. This paper is a continuation of 3.Subspaces of Vector Spaces. A subspace W of a vector space V is a su...