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].(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Interchanging Linear Operator and Infinite Sum

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**