Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1198.42032
Wang, Yan Jin; Zhu, Yu Can
$g$-frames and $g$-frame sequences in Hilbert spaces. (English)
[J] Acta Math. Sin., Engl. Ser. 25, No. 12, 2093-2106 (2009). ISSN 1439-8516; ISSN 1439-7617/e

Let $U$ and $V$ be two complex Hilbert spaces, let $\{V_j\}_{j\in J}$ be a sequence of closed subspaces of $V,$ where $J\subset\Bbb Z,$ and let $L(U,V_j)$ be the collection of all bounded linear spaces from $U$ to $V_j.$ For a $g$-frame $\{\Lambda_j:\Lambda_j\in L(U,V_j)\}_{j\in J}$ for $V$ with respect to $\{V_j\}_{j\in J}$ (i.e. there exist $A,B>0$ such that $$A\Vert f\Vert^2\leq \sum_{j\in J}\Vert \Lambda_jf\Vert^2\leq B\Vert f\Vert^2$$ for all $f\in V)$ the authors find some relations between operators $$S: f\to \sum_{j\in J}\Lambda^*_j\Lambda_jf,\quad Q: \{g_j\}_{j\in J}\to \sum_{j\in J}\Lambda_j^*g_j$$ and $A,B;$ moreover necessary and sufficient conditions for a $g$-frame in terms of $Q$ are given. \par Further the authors define a $g$-frame sequence $\{\Lambda_j\}_{j\in J}$ for $U$ as a $g$-frame for $$W=\overline{\{\sum_{j\in J_1}\Lambda_j^*g_j \,\text{for any finite} \,J_1\subset J \,\text{and any} \,g_j\in V_j,\: j\in J\}}.$$ They discuss that definition and consider the stability of a $g$-frame sequence under perturbation.
[Alexei Lukashov (Istanbul)]

MSC 2000:: *42C15 Series and expansions in general function systems
46C99 Inner product spaces, Hilbert spaces

Keywords: frame; $g$-Bessel sequence; $g$-frame; $g$-frame sequence

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]