*-g-frames in tensor products of Hilbert C*-modules

Rossafi, Mohamed; Kabbaj, Samir

doi:10.2478/aupcsm-2018-0002

Abstract

In this paper, we study ∗-g-frames in tensor products of Hilbert C∗-modules. We show that a tensor product of two ∗-g-frames is a ∗-g-frame, and we get some result.

References

[1] Alijani, Azadeh. “Generalized frames with 𝒞∗-valued bounds and their operator duals.” Filomat 29, no. 7 (2015): 1469–1479. Cited on 17.10.2298/FIL1507469A
Search in Google Scholar Back to article
[2] Alijani, Azadeh, and Mohammad Ali Dehghan. “𝒢-frames and their duals for Hilbert 𝒞∗-modules. Bull. Iranian Math. Soc. 38, no. 3 (2012): 567–580. Cited on 17, 19 and 20.
Search in Google Scholar Back to article
[3] Asgari, Mohammad Sadegh, and Amir Khosravi. “Frames and bases of subspaces in Hilbert spaces.” J. Math. Anal. Appl. 308, no. 2 (2005): 541–553. Cited on 17.10.1016/j.jmaa.2004.11.036
Search in Google Scholar Back to article
[4] Bounader, Nordine, and Samir Kabbaj. “∗-g-frames in hilbert 𝒞∗-modules.” J. Math. Comput. Sci. 4, no. 2 (2014) 246–256. Cited on 17 and 19.
Search in Google Scholar Back to article
[5] Christensen, Ole. An introduction to frames and Riesz bases. Applied and Numerical Harmonic Analysis. Boston, MA: Birkhäuser Boston, Inc. 2003. Cited on 18.10.1007/978-0-8176-8224-8
Search in Google Scholar Back to article
[6] Christensen, Ole, and Yonina C. Eldar. “Oblique dual frames and shift-invariant spaces.” Appl. Comput. Harmon. Anal. 17, no. 1 (2004): 48–68. Cited on 17.10.1016/j.acha.2003.12.003
Search in Google Scholar Back to article
[7] Conway, John B. A course in operator theory. Vol. 21 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society, 2000. Cited on 18.
Search in Google Scholar Back to article
[8] Davidson, Kenneth R. 𝒞∗-algebras by example. Vol. 6 of Fields Institute Monographs. Providence, RI: American Mathematical Society, 1996. Cited on 18 and 20.10.1090/fim/006
Search in Google Scholar Back to article
[9] Duffin, Richard J., and A. C. Schaeffer. “A class of nonharmonic Fourier series.” Trans. Amer. Math. Soc. 72 (1952): 341–366. Cited on 17.10.1090/S0002-9947-1952-0047179-6
Search in Google Scholar Back to article
[10] Frank, Michael, and David R. Larson. “A module frame concept for Hilbert C∗-modules.” In Contemp. Math.247, 207–233. Providence, RI: Amer. Math. Soc., 1999. Cited on 17.10.1090/conm/247/03803
Search in Google Scholar Back to article
[11] Gabor, Denis. “Theory of communications.” Journal of the Institution of Electrical Engineers 93 (1946): 429–457. Cited on 17.10.1049/ji-3-2.1946.0076
Search in Google Scholar Back to article
[12] Hsu, Ming-Hsiu, and Ngai-Ching Wong. “Inner products and module maps of Hilbert 𝒞∗-modules.” Matimyas Matematika 34, no. 1-2 (2011): 56–62. Cited on 24.
Search in Google Scholar Back to article
[13] Khosravi, Amir, and Behrooz Khosravi. “Frames and bases in tensor products of Hilbert spaces and Hilbert 𝒞∗-modules.” Proc. Indian Acad. Sci. Math. Sci. 117, no. 1 (2007): 1–12. Cited on 18 and 20.10.1007/s12044-007-0001-5
Search in Google Scholar Back to article
[14] Khosravi, Amir, and Behrooz Khosravi. “Fusion frames and g-frames in Hilbert 𝒞∗-modules.” Int. J. Wavelets Multiresolut. Inf. Process. 6, no. 3 (2008): 433–446. Cited on 17 and 18.10.1142/S0219691308002458
Search in Google Scholar Back to article
[15] Lance, E. Christopher. Hilbert 𝒞∗-modules. A toolkit for operator algebraists. Vol 210 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 1995. Cited on 19 and 20.
Search in Google Scholar Back to article
[16] Li, Shidong, and Hidemitsu Ogawa. “Pseudoframes for subspaces with applications.” J. Fourier Anal. Appl. 10, no. 4 (2004): 409–431. Cited on 17.10.1007/s00041-004-3039-0
Search in Google Scholar Back to article

-g-frames in tensor products of Hilbert C-modules

Abstract

Paradigm

My account