Abstract
Gram-Schmidt orthonormalization in Banach spaces is considered. Using this orthonormalization process we can prove that if $P$ is a projection on a reflexive Banach space $X$ with a basis $\{e_n;f_n\}$, then there exists a basis $\{u_n;g_n\}$ of $X$ such that $\{g_n\}\approx\{f_n\}$ and the matrix of $P$ with respect to $\{u_n;g_n\}$ has the property that all but a finite number of entries of each column and each row are zero.
Citation
Ying-Hsiung Lin. "GRAM-SCHMIDT PROCESS OF ORTHONORMALIZATION IN BANACH SPACES." Taiwanese J. Math. 1 (4) 417 - 431, 1997. https://doi.org/10.11650/twjm/1500406120
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