<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g- frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C' can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown. </p></abstract>

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g- frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C' can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

Department of Mathematics, University of Maragheh, Maragheh, Iran

Department of Mathematics, Ilam University, Ilam, Iran

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Controlled G-Frames and Their G-Multipliers in Hilbert spaces"}

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine...

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

Published Online: Sep 19, 2013

Page range: 223 - 236

DOI: https://doi.org/10.2478/auom-2013-0035

Keywords
Frame, g-frame, g-Bessel, g-Riesz basis, g-orthonormal basis, multiplier, Schatten p-class, Hilbert-Schmidt, trace class, controlled frame, weighted frame, controlled g-frame, (C,C')-controlled g-frame, (C,C')-controlled g-multiplier operator

This content is open access.

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

Published Online: Sep 19, 2013

Page range: 223 - 236

DOI: https://doi.org/10.2478/auom-2013-0035

KeywordsFrame, g-frame, g-Bessel, g-Riesz basis, g-orthonormal basis, multiplier, Schatten p-class, Hilbert-Schmidt, trace class, controlled frame, weighted frame, controlled g-frame, (C,C')-controlled g-frame, (C,C')-controlled g-multiplier operator

This content is open access.

Keywords
Frame, g-frame, g-Bessel, g-Riesz basis, g-orthonormal basis, multiplier, Schatten p-class, Hilbert-Schmidt, trace class, controlled frame, weighted frame, controlled g-frame, (C,C')-controlled g-frame, (C,C')-controlled g-multiplier operator