We introduce the concept of K-g-frames in Hilbert spaces and study the essential distinctions between K-g-frames and g-frames. Then we characterize K-g frames by using dual g-frames of special closed subspaces and give a way to construct dual g-frames for special closed subspaces. Finally, we study some properties of K-g frames.
Yan ZHOU, Yu Can ZHU. K-g-Frames and Dual g-Frames for Closed Subspaces. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 799-806 https://doi.org/10.12386/A2013sxxb0078
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Benedetto J., Powell A., Yilmaz O., Sigma-delta quantization and finite frames, IEEE Trans. Inf. Theory, 2006, 52: 1990-2005. [2] Candés E. J., Donoho D. L., New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities, Comm. Pure Appl. Math., 2004, 56: 216-266. [3] Cao H. X., Li L., Chen Q. J., Ji G. X., (p, Y )-operator frames for a Banach space, J. Math. Anal. Appl., 2008, 347: 583-591. [4] Christensen O., Goh S. S., Pairs of oblique duals in spaces of periodic functions, Adv. Comput. Math., 2010 32: 353-379. [5] Douglas R. G., On majorization factorization and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 1966, 17(2): 413-415. [6] Duffin R. J., Schaeffer A. C., A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 1952, 72: 341-366. [7] Găvruta P., Frames for operators, Appl. Comput. Harmon. Anal., 2012, 32: 139-144. [8] Găvruta P., On the duality of fusion frames, J. Math. Anal. Appl., 2007, 333(2): 871-879. [9] Guo Z. H., Cao H. X., Yin J. C., Stability of (p, Y )-operator frames, Journal of Mathematical Research Exposition, 2011, 31(3): 535-544. [10] Heath R. W., Paulraj A. J., Linear dispersion codes for MIMO systems based on frame theory, IEEE Trans. Signal. Process, 2002, 50: 2429-2441. [11] Li J. Z., Zhu Y. C., g-Riesz frames in Hilbert spaces, Scientia Sinica Mathematica, 2011, 41(1): 53-68 (in Chinese). [12] Lopez J., Han D., Optimal dual frames for erasures, Linear Algebra Appl., 2010, 432: 471-482. [13] Mallat S., A Wavelet Tour of Signal Processing, Second Edition, Academic Press, San Diego, 2000. [14] Pedro G. M., Mariano A. R., Demetrio S., Duality in reconstruction systems, Linear Algebra Appl., 2012, 436: 447-464. [15] Sun W. C., g-frames and g-Riesz bases, J. Math. Anal. Appl., 2006, 322(1): 437-452. [16] Yu B. Y., Su Z. B., Construction of dual g-frames for closed subspaces, Int. J. Wavelets Multiresolut. Inf. Process, 2011, 9(6): 947-964. [17] Zang L. L., Sun W. C., Invertible sequences of bounded linear operators, Acta Mathematica Scientia, 2011, 31B(5): 1939-1944. [18] Zhu Y. C., Characterizations of g-frames and g-Riesz bases in Hilbert spaces, Acta Mathematica Sinica, English Series, 2008, 24(10): 1727-1736.