Basis projection ( $P_{n}$ )

The nth basis projection associated with a Schauder basis is

P_{n} (\sum_{k = 1}^{\infty} a_{k} e_{k}) = \sum_{k = 1}^{n} a_{k} e_{k} .

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- Basis constant Basis projection

Basis constant

The basis constant of a Schauder basis is

sup_{n} ∥ P_{n} ∥

, where

P_{n}

are its basis projections. Uniform boundedness makes this supremum finite.

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