We prove that a dictionary for a Banach space $X$ has the strong coefficient quantization property if it has the same property when it restricted on the unit ball of $X$. We also obtain the same result for the strong net quantization property.
References
P.G. Casazza, S.J. Dilworth, E. Odell, T. Schlumprecht and A. Zsák, Coefficient quantization for frames in Banach Spaces, J. Math. Anal. Appl. 348 (2008), 66–86. MR2449328 10.1016/j.jmaa.2008.06.055 P.G. Casazza, S.J. Dilworth, E. Odell, T. Schlumprecht and A. Zsák, Coefficient quantization for frames in Banach Spaces, J. Math. Anal. Appl. 348 (2008), 66–86. MR2449328 10.1016/j.jmaa.2008.06.055
S.J. Dilworth, E. Odell, T. Schlumprecht and A. Zsák, Coefficient Quantization in Banach Spaces, Found. Comput. Math. 8 (2008), 703–736. MR2461244 10.1007/s10208-007-9002-0 S.J. Dilworth, E. Odell, T. Schlumprecht and A. Zsák, Coefficient Quantization in Banach Spaces, Found. Comput. Math. 8 (2008), 703–736. MR2461244 10.1007/s10208-007-9002-0
