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Let $(e_n)_{n \in \mathbb{N}}$ be the standard basis of $\ell^2$ with basis constant $K_b=1$

We know that also $(ne_n)_{n \in \mathbb{N}}$ is a Schauder basis of $\ell^2$

My question is: what's the basis constant $K_b$ of $(ne_n)_{n \in \mathbb{N}}$ ?

Thanks.

Matey Math
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  • What is the definition of 'basis constant' ? – daw Jan 11 '23 at 13:04
  • @daw It's the sup of the partial sum projections associated to a basis, the concept concerns the Schauder basis (Topics In Banach Space Theory - Albiac, Kalton, page 5) – Matey Math Jan 11 '23 at 13:10
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    I believe the answer comes directly from the definition. So please state it. See also https://math.stackexchange.com/questions/644945/the-importance-of-basis-constant , which basically tells you that $K=1$ for $(ne_n)$. – daw Jan 11 '23 at 14:06
  • Ok @daw thanks for your answer – Matey Math Jan 11 '23 at 14:10

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