Are there practical applications for l2 in mathematics and physics?

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Discussion Overview

The discussion centers around the practical applications of l2, the set of square summable sequences, in mathematics and physics. Participants explore its relevance in quantum mechanics, general physics, and numerical analysis, while also considering its theoretical significance.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant seeks applications of l2 beyond its theoretical aspects, particularly in quantum mechanics and numerical analysis.
  • Another participant suggests that l2 serves primarily as a source of examples with properties similar to other spaces, indicating limited practical applications.
  • A later reply mentions that while l2 may not have strict applications, studying it can provide insights into separable Hilbert spaces, which are significant in physics.

Areas of Agreement / Disagreement

Participants express differing views on the practical applications of l2. Some argue that its applications are minimal, while others suggest that its study is valuable for understanding broader concepts in physics.

Contextual Notes

There is an acknowledgment of the elegance of l2 in pure mathematics, but the discussion highlights a lack of consensus on its practical utility. The conversation also touches on the importance of separable Hilbert spaces in physics without resolving the extent of l2's applications.

sparkster
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Hi all. I heard about the site the the Sec Web. Anyway, I'm a math major with philosophy and physics minors, and I'm going to grad school in math this fall.

I'm doing my senior seminar on l2, the set of square summable sequences. I'd like to close my paper and my talk on some applications, but I can't find anything. I know that L2 has some apps for QM, but is there anything you can do with l2? Anything with QM, general physics, or numerical analysis?
Thanks in advance.
 
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Not really. The main application of l2as well as general ln is as simpler sources of examples having the properites of Ln
 
Originally posted by HallsofIvy
Not really. The main application of l2as well as general ln is as simpler sources of examples having the properites of Ln
So there's nothing you can do with l2? Don't get me wrong, I'm enough a (potential) pure mathematician to appreciate the elegance of l2 absent any applications, but it's be nice to have something.



ps,
Is there a list of code for the math symbols.
 
Not in the strictest sence, no, but since every seperable Hilbert space is isomorfic to l², if you study this little guy you've studied them all, as my analysis professor so nicely said.

And since separable Hilbert-spaces are important in physics (like the aformentioned L²), it does have a use since some properties might be easier studied in l².
 

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