Geodesic
ON A PROPERTY OF BASES IN A HILBERT SPACE
Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 177-180

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DOI

In this paper we study a seemingly unnoticed property of bases in a Hilbert space that falls in the general area of constructing new bases from old, yet is quite atypical of others in this regard. Namely, if $\{x_n\}$ is any normalized basis for a Hilbert space $ H $ and $ \{\,f_n\}$ the associated basis of coefficient functionals, then the sequence $\{x_n+f_n\} $ is again a basis for $ H $. The unusual aspect of this observation is that the basis $ \{x_n+f_n\} $ obtained in this way from $\{x_n\} $ and $ \{\,f_n\} $ need not be equivalent to either, in contrast to the standard techniques of constructing new bases from given ones by means of an isomorphism on $ H $. In this paper we study bases of this form and their relation to the component bases $ \{x_n\} $ and $ \{\,f_n\}$.
DOI : 10.1017/S0017089503001691
Mots-clés : Primary 46C05, 46B15, 47B99 
HOLUB, JAMES R. ON A PROPERTY OF BASES IN A HILBERT SPACE. Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 177-180. doi: 10.1017/S0017089503001691
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     journal = {Glasgow mathematical journal},
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     year = {2004},
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     doi = {10.1017/S0017089503001691},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001691/}
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