Space of square-summable sequences

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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=1R or
  • (xn)n=1C

With the property of:

  • n=1|xi|2<

Usual inner product

This space is usually equipped[1] with the following inner product:

  • For x,yl2 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

  1. Jump up to: 1.0 1.1 Functional Analysis - George Bachman and Lawrence Narici