What is an example of a Banach space that is not a BK space?

A norm space $X$ is BK Space, if $X$ is Banach space and for all natural numbers n, $p_n(\bar{x}) = x_n$ is continuous, for all $\bar{x}$ in X.

What is an example of a Banach space that is not a BK-space?

A normed sequence space $X$ (with projections $p_n$) is a BK Space if $X$ is Banach space and for all natural numbers $n$, $p_n(\bar{x}) = x_n$ is continuous, for all $\bar{x}$ in $X$.

Norm space X is BK Space, if X is Banach space and for all natural number n, $p_n(\bar{x}) = x_n$ is continuous, for all $\bar{x}$ in X.

What is an example of a Banach space that is not a BK space?

A norm space $X$ is BK Space, if $X$ is Banach space and for all natural numbers n, $p_n(\bar{x}) = x_n$ is continuous, for all $\bar{x}$ in X.