Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 2, Issue 2, August 2018, Pages: 52-60

K-operator Frame for End*A(H)

Mohamed Rossafi and Samir Kabbaj

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


Frames generalize orthonormal bases and allow representation of all the elements of the space. Frames play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicine, and probability. In this paper, we introduce the concepts of K-operator frame for the space End*A(H) of all adjointable operators on a Hilbert A-module H and we establish some results.


K-frame, K-operator frame, C* -algebra, Hilbert A-modules



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

2. O. Christensen, An Introduction to Frames and Riesz bases, Brikh¨auser, 2016.

3. F. R. Davidson, C∗ -algebra by example, Fields Ins. Monog. 1996.

4. J.B.Conway, A Course In Operator Theory, AMS, 21, 2000.

5. R. J. Duffin and 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. Oper. Theory 48 (2002), 273-314.

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

8. I. Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-858.

9. A. Khosravi and 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. Najati, M. M. Saem and P. Gavruta, Frames and operators in Hilbert C∗ -modules, Oam, 10(1) (2016), 73-81.

11. W. Paschke, Inner product modules over B∗ -algebras, Trans. Amer. Math. Soc., 182(1973), 443-468.

12. L. C. Zhang, The factor decomposition theorem of bounded generalized inverse modules and their topological continuity, J. Acta Math. Sin., 23 (2007), 1413-1418.

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