- #1
logarithmic
- 107
- 0
Suppose that [itex]x\in H[/itex], where H is a Hilbert space. Then x has an orthogonal decomposition [itex]x = \sum_{i=0}^\infty x_i[/itex].
I have a linear operator P (more specifically a projection operator), and I want to write:
[itex]P(x) = \sum_{i=0}^\infty P(x_i)[/itex].
How can I justify taking the operator inside the infinite sum?
I have a linear operator P (more specifically a projection operator), and I want to write:
[itex]P(x) = \sum_{i=0}^\infty P(x_i)[/itex].
How can I justify taking the operator inside the infinite sum?