arXiv subjects

Diana T. Stoeva

Publications and source records attributed to Diana T. Stoeva.

23 records · Page 2Linked to original sources

arXiv2010

Classification of General Sequences by Frame-Related Operators

This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We investigate these operators for arbitrary sequences, which in general lead to possibly unbounded operators. We characterize various classes of sequences in terms of these operators and vice-versa. Finally, we classify these sequences by operators applied on orthonormal bases.

math.FA↗

arXiv2010

Detailed characterization of unconditional convergence and invertibility of multipliers

In this paper we investigate the possibility of unconditional convergence and invertibility of multipliers $M_{m,Φ,Ψ}$ depending on the properties of the sequences $Ψ$,$Φ$ and $m$. We characterize a complete set of conditions for the invertibility and the unconditional convergence of multipliers, and collect those results in tables. We either prove that unconditional convergence and invertibility is not possible, that one or both of these conditions are always the case for the given parameters, or we give examples for the feasible combinations. We give a full list of examples for all conditions.

math.FA↗

arXiv2009

Perturbation of frames in Banach spaces

In this paper we consider perturbation of X_d-Bessel sequences, X_d-frames, Banach frames, atomic decompositions and X_d-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.

math.FA↗

arXiv2008

On sequence spaces for Fréchet frames

We analyze the construction of a sequence space $\widetildeΘ$, resp. a sequence of sequence spaces, in order to have $\{g_i\}$ as a $\widetildeΘ$-frame or Banach frame for a Banach space $X$, resp. pre-$F$-frame or $F$-frame for a Fréchet space $X_F=\cap_{s\in {\mathbb N}_0} X_s$, where $\{X_s\}_{s\in {\mathbb N}_0}$ is a sequence of Banach spaces.

math.FA↗

arXiv2008

Series expansions in Fréchet spaces and their duals; construction of Fréchet frames

Frames for Fréchet spaces $X_F$ with respect to Fréchet sequence spaces $Θ_F$ are studied and conditions, implying series expansions in $X_F$ and $X_F^*$, are determined. If $\{g_i\}$ is a $Θ_0$-frame for $X_0$, we construct a sequence $\{X_s\}_{s\in {\mathbb N}_0}$, $X_s\subset X_{s-1}$, $s\in {\mathbb N}$, for given $Θ_F$, respectively a sequence $\{Θ_s\}_{s\in {\mathbb N}_0}$, $Θ_s\subset Θ_{s-1}$, $s\in {\mathbb N}$, for given $X_F$, so that $\{g_i\}$ is a pre-$F$-frame (or $F$-frame) for $X_F$ with respect to $Θ_F$ under different assumptions given on $X_0$, $Θ_0$, $Θ_F$ or $X_0$, $Θ_0$, $X_F$.

math.FA↗