Editing F-space (section)

=== Example 2 ===

Let <math>W_p(\mathbb{D})</math> be the space of all complex valued [[Taylor series]]
<math display=block>f(z) = \sum_{n \geq 0} a_n z^n</math>
on the unit disc <math>\mathbb{D}</math> such that
<math display=block>\sum_n \left|a_n\right|^p < \infty</math>
then for <math>0 < p < 1,</math> <math>W_p(\mathbb{D})</math> are F-spaces under the [[p-norm]]:
<math display=block>\|f\|_p = \sum_n \left|a_n\right|^p \qquad (0 < p < 1).</math>

In fact, <math>W_p</math> is a [[quasi-Banach algebra]]. Moreover, for any <math>\zeta</math> with <math>|\zeta| \leq 1</math> the map <math>f \mapsto f(\zeta)</math> is a bounded linear (multiplicative functional) on <math>W_p(\mathbb{D}).</math>