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I'm interested in Operator Algebras and mathematical physics; recently, a friend showed me Duren and Schuster's "Bergman Spaces". I've read about two chapters now and I see there is a nice play between functional analysis, operator theory and complex variables.

But what are the applications of this subject elsewhere?
Would the average professional operator theory person know much about this?
Does it come up in theoretical physics?

Squirtle
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  • Why are operator algebras interesting (genuine question)? Can you motivate them without using "big words"? – bzm3r Jun 19 '14 at 22:08
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    Well, I suppose that the reason I find operator algebras interesting is because of its presence in quantum mechanics and I just like the feel of the math in op. algs. – Squirtle Jun 19 '14 at 22:11
  • I have noticed that a new tag ([tag:bergman-spaces]) was created. (At the moment, it is used here and here.) I considered adding the tag to this question, but since it already has 5 tags, I leave the decision to you. (Should the tag be added? If yes, which tag should be replaced?) – Martin Sleziak Jun 03 '15 at 05:20
  • Seems like Leo Sera (who edited this post) added the tag, I don't see many things on bergman spaces... however that may change in time. I'd just leave it as is and I'll take down another tag. – Squirtle Jun 03 '15 at 14:54

1 Answers1

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Bergman spaces have applications in problems of quantization. For details see, for example this paper Berezin and Berezin-Toeplitz Quantizations for General Function Spaces

Some general description of quantization from mathematical point of view is here Quantization Methods: A Guide for Physicists and Analysts

hjhjhj57
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Maerorek
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