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I have read several histories of functional analysis and operator theory, and they all focus on the importance of Hilbert's spectral theory, Frechet's metric spaces, Lebesgue integration theory, and unification work by Riesz. This work was all done about 100 years ago so I'm wondering what major advances have happened since? From reading these histories you'd get the impression that nothing of major note has happened in these fields since around 1940.

So what topics do modern specialists in functional analysis and operator theory perform research in? Is it the case that all the widely applicable results were discovered 100 years ago and nowadays its all finding results in niche areas? Are there any recommendations for papers written in the last 20 years which are considered to be of major importances? What about some recent (last 5 years) papers that are worth reading?

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    From my understanding, the functional analysis modern research has now become the control theory and the analysis of PDE. – 2017-02-08
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    @anonymus: I respectfully disagree. I have known functional analysts working on PDE-unrelated issues ([here](http://math.stackexchange.com/a/827766/8157) is an example). [There is also this expository blog post by Tim Gowers](https://gowers.wordpress.com/2009/02/07/a-remarkable-recent-result-in-banach-space-theory/) which might be interesting. – 2017-02-08
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    @GiuseppeNegro thanks for the link. It's quite interesting. Anyway, i don't know any researcher who is working on pure functional analysis. That is what brought my first comment. – 2017-02-08
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    So once the 100 year old theory is learned, that's it, from then on its all about applying it to PDEs and control theory? – 2017-02-08
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    The 100 year old theories of Functional Analysis grew directly out of making sense of the 200 year old PDE/ODE theories of Fourier and others. So it should not be a surprise that the fields feed off each other, even though they're independent. Here's a journal to look at: http://www.sciencedirect.com/science/journal/00221236 – 2017-02-08
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    Besides, @eurocoder: have a look at the links I provided, if you want. They are about modern functional analytic research that has little to do with PDEs and similar. – 2017-02-08
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    @GiuseppeNegro ok thanks, I will take a look at them now. – 2017-02-10

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