# Strobl18

Harmonic Analysis and Applications

June 4-8, 2018

Strobl, AUSTRIA

### "Controlled fusion frames in Hilbert C*-modules"

#### Rashidi-Kouchi, Mehdi

Weighted and controlled frames in Hilbert spaces have been introduced in [1] to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces, however they are used earlier in [2] for spherical wavelets. The concept of controlled frames has been extended and generalized to g-frames in [3] and fusion frames in [4]. Hilbert $C^*$-modules form a wide category between Hilbert spaces and Banach spaces. Frames and their generalization are defined in Hilbert $C^*$-modules and some properties have been studied for example see [5]. Here we investigate basic properties of controlled fusion frames in Hilbert $C^*$-modules. Also we present a characterization of controlled fusion frames for Hilbert $C^*$-modules and show that any controlled fusion frame in Hilbert $C^*$-module is frame in Hilbert $C^*$-module. {\bf References:} \begin{itemize} \item[{[1]}] P. Balazs, J-P. Antoine and A. Grybos: Wighted and Controlled Frames, \emph{Int. J. Wavelets, Multiresolut. Inf. Process.}, 8(1) (2010), 109--132. \item[{[2]}] I. Bogdanova, P. Vandergheynst, J.P. Antoine, L. Jacques, M. Morvidone: Stereographic wavelet frames on the sphere, \emph{Applied Comput. Harmon. Anal.} 19, (2005), 223--252. \item[{[3]}] A. Rahimi and A. Fereydooni: Controlled G-Frames and Their G-Multipliers in Hilbert spaces, \emph{An. St. Univ. Ovidius Constanta}, 21(2), (2013), 223--236 . \item[{[4]}] A. Khosravi and K. Musazadeh: Controlled fusion frames, \emph{ Methods of Functional Analysis and Topology}, 18(3), (2012), 256--265. \item[{[5]}] M. Rashidi-Kouchi, A. Nazai, M. Amini: On stability of g-frames and g-Riesz bases in Hilbert $C^*$-modules, \emph{Int. J. Wavelets Multiresolut. Inf. Process}, 12(6), (2014), 1--16. \end{itemize}
http://univie.ac.at/projektservice-mathematik/e/talks/Rashidi-Kouchi_2018-01_Rashidi-Kouchi_Mehdi.pdf

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