Space of square-summable sequences
From Maths
Definition
The space of square-summable sequences, denoted l2, is the space of all (countable) sequences of either complex, or real numbers[1]. That is:
- (xn)∞n=1⊂R or
- (xn)∞n=1⊂C
With the property of:
- ∞∑n=1|xi|2<∞
Usual inner product
This space is usually equipped[1] with the following inner product:
- For x,y∈l2 we define ⟨x,y⟩:=∑∞n=1xi¯yi
Proving this requires things like Holder's inequality (with the funny o) and is something I need to do:
TODO: Page 9 is a start of the first ref
References
- ↑ Jump up to: 1.0 1.1 Functional Analysis - George Bachman and Lawrence Narici