$\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules

Subject Areas : Functional analysis

M. Rossafi ¹ , S. Kabbaj ²

1 - Department of Mathematics, University of Ibn Tofail, B.P. 133, Kenitra, Morocco
2 - Department of Mathematics, University of Ibn Tofail, B.P. 133, Kenitra, Morocco

Received: 2017-12-26 Accepted : 2018-03-17 Published : 2018-03-01

Keywords: Frame, $ast$-g-frame, $ast$-K-g-frame, Hilbert $\mathcal{A}$-modules,

Abstract :

In this paper, we introduce the concepts of $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules and we establish some results.

References:

[1] A. Alijani, M. A. Dehghan, *-frames in Hilbert C*-modules, U.P.B. Sci. Bull. (Ser. A). 73 (4) (2011), 89-106.

[2] A. Alijani, Generalized frames with C*-valued bounds and their operator duals, Filomat. 29 (7) (2015), 1469-1479.

[3] O. Christensen, An introduction to frames and Riesz bases, Brikhouser, 2016.

[4] J. B. Conway, A course in operator theory, AMS, 2000.

[5] F. R. Davidson, C*-algebra by example, Fields Ins. Monog, 1996.

[6] R. J. Duffin, A. C. Schaeffer, A class of nonharmonic fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.

[7] M. Frank, D. R. Larson, Frames in Hilbert C*-modules and C*-algebra, J. Operator Theory. 48 (2002), 273-314.

[8] L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012), 139-144.

[9] A. Khosravi, B. Khosravi, Frames and bases in tensor products of Hilbert spaces and Hilbert C*-modules, Proc. Indian Acad. Sci. Math. Sci. 117 (2007), 1-12.

[10] A. Khosravi, B. Khosravi, Fusion frames and g-frames in Hilbert C*-modules, Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008), 433-446.

[11] E. C. Lance, Hilbert C*-modules, A toolkit for operator algebraists, Cambridge University Press, 1995.

[12] A. Najati, M. M. Saem, P. Gavruta, Frames and operators in Hilbert C*-modules, Oam. 10 (1) (2016), 73-81.