Class of bounded operators associated with an atomic system

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Published: Mar 22, 2014
DOI: https://doi.org/10.5556/j.tkjm.46.2015.1601
Keywords:
Bessel sequences frames atomic systems K-Frames.

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P.Sam Johnson
G. Ramu

Abstract

$K$-frames, more general than the ordinary frames, have been introduced by Laura G{\u{a}}vru{\c{t}}a in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Using the frame operator, we find a class of bounded linear operators in which a given Bessel sequence is an atomic system for every member in the class.

Article Details

How to Cite
Johnson, P., & Ramu, G. (2014). Class of bounded operators associated with an atomic system. Tamkang Journal of Mathematics, 46(1), 85–90. https://doi.org/10.5556/j.tkjm.46.2015.1601
Issue
Vol. 46 No. 1 (2015)
Section
Papers
Author Biographies

P.Sam Johnson

Department ofMathematical andComputational Sciences,National Institute of Technology Karnataka, Surathkal, Mangalore 575 025, India.

G. Ramu

Department ofMathematical andComputational Sciences,National Institute of Technology Karnataka, Surathkal, Mangalore 575 025, India.

References

R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72(1952),341--366.

I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27(1986), 1271-1283.

P. Ferreira, Mathematics for multimedia signal processing II: Discrete finite frames and signal reconstruction, Byrnes, J.S. (ed.) 17(1999), 35-54.

Y. C. Eldar, Sampling with arbitrary sampling and reconstruction spaces and oblique dual frame vectors, J. Fourier Anal. Appl., 9 (2003), 77--96.

T. Strohmer and R. W. Heath, Jr., Grassmannian frames with applications to coding and communication, Appl. Comput. Harmon. Anal., 14 (2003), 257--275.

X. Xiao, Y. Zhu, L. Gv avruc ta, Some properties of K-frames in Hilbert spaces, Results Math., 63(2013), 1243-1255.

O. Christensen, An introduction to frames and Riesz bases, Applied and Numerical Harmonic Analysis, Birkhauser Boston Inc.,Boston, MA, 2003.

L. Gv avruc ta, Frames for operators, Appl. Comput. Harmon. Anal., 32 (2012), 139-144.

P. G. Casazza, The art of frame theory, Taiwanese J. Math., 4 (2000), 129--201.

R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc.,17(1966), 413--415.