Some Generalizations of Frames in Hilbert Modules

Frames play significant role in various areas of science and engineering. In this paper, we introduce the concept of frames for the set of all adjointable operators from ℋ to K and their generalizations. Moreover, we obtain some new results for generalized frames in Hilbert modules.

[1]  D. Larson,et al.  Riesz bases and their dual modular frames in Hilbert C∗-modules , 2008 .

[2]  Azadeh Alijani.  GENERALIZED FRAMES WITH C*-VALUED BOUNDS AND THEIR OPERATOR DUALS , 2015 .

[3]  Behrooz Khosravi,et al.  Fusion Frames and G-Frames in Hilbert C*-Modules , 2008, Int. J. Wavelets Multiresolution Inf. Process..

[4]  I. Daubechies,et al.  PAINLESS NONORTHOGONAL EXPANSIONS , 1986 .

[5]  Behrooz Khosravi,et al.  G-Frames and Modular Riesz Bases in Hilbert C*-Modules , 2012, Int. J. Wavelets Multiresolution Inf. Process..

[6]  M. Janfada,et al.  Frames for operators on Hilbert modules , 2014, 1408.6468.

[7]  D. Gabor,et al.  Theory of communication. Part 1: The analysis of information , 1946 .

[8]  M. Frank.  FRAMES FOR HILBERT C*-MODULES , 2004 .

[9]  J. Conway.  A course in operator theory , 1999 .

[10]  M. Dehghan,et al.  G-frames as special frames , 2013, Turkish Journal of Mathematics.

[11]  Irving Kaplansky,et al.  Modules Over Operator Algebras , 1953 .

[12]  Ljiljana Arambašić.  On frames for countably generated Hilbert C*-modules , 2006 .

[13]  W. Jing.  Frames In Hilbert C*-modules , 2006 .

[14]  FRAMES IN HILBERT C*-MODULES AND C*-ALGEBRAS , 2000, math/0010189.

[15]  O. Christensen.  An introduction to frames and Riesz bases , 2002 .

[16]  R. Duffin,et al.  A class of nonharmonic Fourier series , 1952 .

[17]  Zhong-Qi Xiang.  G-frames for operators in Hilbert C ∗-modules , 2016 .

[18]  Dennis Gabor,et al.  Theory of communication , 1946 .

[19]  A. Khosravi,et al.  Bessel multipliers in Hilbert $C^\ast$--modules , 2015 .