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to the functional analysis crew of the $n$Lab: where should operator spectrum point to? Do we have any suitable entry?
Well you may try to decide between spectral theory which is more general, and spectral theorem which is more specific. In future we could have separate entries for versions like spectral theorem for bounded normal operators, for families etc.
So you are saying I should put redirects? I was hoping sombody would feel inspired to create at least a stub for operator spectrum
No, I am saying that the term “operator spectrum” is a bit sidetrack form the organization we have started here. There is a classical subject of spectral theorems for various kinds of operators which belong to spectral theorem entry, just as on wikipedia. On the other hand, spectral theory is wider subject and most of the things are about families of operators, algebras of operators, spectra of Banach algebras, of C*-algebras and so on. It would be superfluous to mess up with orthogonal entry with vague associative name like “operator spectrum” (what is it ? a spectrum of an operator ? a spectrum of an operator algebra ? any spectrum appearing in operator theory ?). At the least I could agree with a name like spectrum of an operator, but writing an entry for it would most likely boil down to writing spectral theorem. So, until we have so much material to go into a reorganization I would vote for a redirect of your choice.
By the way there is a recent entry spectral theorem for bounded selfadjoint operators (zoranskoda). I am taking it back a bit. spectrum of an operator should exist as a separate entry (separate from spectral theorem), though it is not easy to write it. In any case operator spectrum is not a good term.
OK, there is a new entry spectrum of an operator with the redirect (though I am not real happy with the redirect) operator spectrum.
OK, there is a new entry
Thanks!!
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