Related papers: Subsequences of frames

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…

In this note, following the theory of discrete frame perturbations in a complex Hilbert space, we examine perturbation of rank $n$ continuous frame, rank $n$ continuous Bessel family and rank $n$ continuous Riesz family in a non-commutative…

We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…

In this paper we consider on the notion of continuous frame of subspace and define a new concept of continuous frame, entitled {\it continuous atomic resolution of identity}, for arbitrary Hilbert space $\h$ which has a countable…

For H a separable infinite dimensional complex Hilbert space, we prove that every B(H) operator has a basis with respect to which its matrix representation has a universal block tridiagonal form with block sizes given by a simple…

We construct a minimal dynamical system of mean dimension equal to $1$, which can be embedded in the shift action on the Hilbert cube $[0,1]^\mathbb{Z}$. This clarifies a seemingly plausible impression about embedding possibility in…

We study edge-isoperimetric inequalities in chamber graphs of affine hyperplane arrangements. Our approach is topological: to a set of chambers we associate its thickening in Euclidean space and estimate its edge boundary through the…

We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form first of a distance function to a random substructure,…

An {\it Omnibus Sequence} of length $n$ is one that has each possible "message" of length $k$ embedded in it as a subsequence. We study various properties of Omnibus Sequences in this paper, making connections, whenever possible, to the…

The space $\mathscr B_{mt}[(m_j)_j,(n_j)_j]$ is a Bourgain-Delbaen space modelled on a mixed Tsirelson space $T[(m_j)_j,(n_j)_j]$ and is a slight modification of $\mathfrak B_{\text{mt}}[(m_j)_j,(n_j)_j]$, a space defined by S. Argyros and…

We prove that every hyperplane passing through the origin in $\rr^{n+1}$ divides an embedded compact free boundary minimal hypersurface of the euclidean $(n+1)$-ball in exactly two connected hypersurfaces. We also show that if a region in…

We remark that if $X$ is an infinite dimensional Banach space then every seminormalized weakly null sequence in $X$ has an asymptotic monotone basic subsequence. We also observe that if $X$ contains an isomorphic copy of $\ell_1$, then for…

A graph $H$ is an \emph{isometric} subgraph of $G$ if $d_H(u,v)= d_G(u,v)$, for every pair~$u,v\in V(H)$. A graph is \emph{distance preserving} if it has an isometric subgraph of every possible order. A graph is \emph{sequentially distance…

Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…

Since persistence diagrams do not admit an inner product structure, a map into a Hilbert space is needed in order to use kernel methods. It is natural to ask if such maps necessarily distort the metric on persistence diagrams. We show that…

A definition of frames in Krein spaces is proposed which extends the concept of $J$-frames defined by J.I. Giribet et al., J. Math. Anal. Appl. ${\textbf{393}}$ (2012), 122-137. The principal difference consists in the fact that a $J$-frame…

A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The basic tools of frame theory are described in the formalism of Krein spaces. It is…

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…