In a Hilbert space $H$, If we define $\{y_n\}$ as $y_{n}=\frac{x_{n}}{\left\|x_{n}\right\|^2} \text { for } n=m \text { and } y_{n}=0 \text { for } n \neq m$, then for any $\{x_n\}\in H$ ,$\{y_n\}$ is a biorthogonal sequence of $\{x_n\}$, is that correct?
2026-04-06 20:59:19.1775509159
Does any sequence in Hilbert space have biorthogonal sequence?
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