Taiwanese Journal of Mathematics

GRAM-SCHMIDT PROCESS OF ORTHONORMALIZATION IN BANACH SPACES

Ying-Hsiung Lin

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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.

Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 417-431.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406120

Digital Object Identifier
doi:10.11650/twjm/1500406120

Mathematical Reviews number (MathSciNet)
MR1486563

Zentralblatt MATH identifier
0908.46008

Subjects
Primary: 46B25: Classical Banach spaces in the general theory

Keywords
equivalent bases process of orthonormalization reduction of matrices of projections

Citation

Lin, Ying-Hsiung. GRAM-SCHMIDT PROCESS OF ORTHONORMALIZATION IN BANACH SPACES. Taiwanese J. Math. 1 (1997), no. 4, 417--431. doi:10.11650/twjm/1500406120. https://projecteuclid.org/euclid.twjm/1500406120


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