$*$-Fusion ‎F‎rames in Hilbert Modules Over Locally $C^*$-Algebras

Subject Areas : International Journal of Industrial Mathematics

طیبه  لعل شاطری ¹ (گروه ریاضی محض، دانشکده ریاضی و علوم کامپیوتر دانشگاه حکیم سبزواری، سبزوار، ایران)

Received: 2018-06-25 Accepted : 2021-02-10 Published : 2021-04-01

Keywords: C*-algebraک Locally C*-algebra, Hilbert C*-module, frame, *-fusion frame,

Abstract :

The main purpose of this paper is to introduce the notion of *-fusion frames in Hilbert modules over locally C*-algebras to study some properties about these frames. We present some results of frames in the view of *-fusion frames in Hilbert modules over locally C*- algebras. inparticular we give the reconstruction formula for these frames.

References:

[1] A. Alijani, M. A. Dehghan, ∗-Frames in Hilbert C∗-modules, U.P.B. Sci. Bull. Series A 73 (2011) 89-106.
[2] M. Azhini, N. Haddadzadeh, Fusion frames in Hilbert modules over pro-C∗-algebras, Int. J. Industrial Mathematics 5 (2013) 112-123.
[3] P. G. Casazza, G. Kutyniok, Frames of subspaces, in Wavelets, Frames and Operator Theory, Contemp. Math. 345 (2004) 87-113.
[4] I. Daubechies, A. Grassman, Y. Meyer, Painless nonothogonal expanisions, J. Math. Phys. 2 (1986) 1271-1283.
[5] R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952) 341-366.
[6] M. Frank, D. R. Larson, Frames in Hilbert C∗-modules and C∗-algebras, J. Operator Theory 48 (2002) 273-314.
[7] A. Inoue, Locally C∗-algebras, Mem. Fac. Sci. Kyushu Univ. Ser. A 25 (1971) 197-235.
[8] M. Joita, On Hilbert modules over locally C∗-algebras II, Periodica Math. Hungarica 51 (2005) 27-36.
[9] A. Khosravi, B. Khosravi, Fusion frames and g-frames in Hilbert C∗-Modules, Int. J. Wavelet, Multiresolution and Information Processing 6 (2008) 433-446.
[10] B. Magajna, Hilbert C∗-modules in which all closed submodules are complemented,Proc. Amer. Math. Soc. 125 (1997) 849-852.
[11] V. M. Manuilov, Adjointability of operators on Hilbert C∗-modules, Acta Math. Univ. Comenianae LXV 2 (1996) 161-169.
[12] A. Nejati, A. Rahimi, Generalized frames in Hilbert spaces, Bull. Iranian Math. Soc. 35 (2009) 97-109.
[13] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (2006) 437-452.
[14] S. Abbasbandy, T. Allahviranloo, Numerical solutions of fuzzy differential equations by taylor method, Computational Methods in Applied Mathematics 2 (2002) 113-124.
[15] D. Dubois, H. Prade, Towards fuzzy differential calculus, Fuzzy Sets and Systems 8 (1982) 1-7.
[16] Y. Lai, C. L. Hwang, Fuzzy Mathematical programming theory and applications, Springer,  Belin, (1992).