Vassil Nikolov | ΠΠ°ΡΠΈΠ» ΠΠΈΠΊΠΎΠ»ΠΎΠ²@vnikolov@ieji.de
@johncarlosbaez@mathstodon.xyz wrote:
In functional analysis and quantum physics, I'd say the definition of 'Hilbert space' is incredibly important!Would you add "bounded operator" on par with it?
@MartinEscardo@mathstodon.xyz
John Carlos Baez@johncarlosbaez@mathstodon.xyz
@vnikolov@ieji.de @MartinEscardo@mathstodon.xyz - I think the idea of 'bounded operator' is kind of obvious compared to the definition of 'Banach space', and in quantum mechanics the deep and important definition is that of 'self-adjoint operator', not necessarily bounded.
In short, I don't think 'bounded operator' is a concept with magical power, while 'Hilbert space' and 'self-adjoint operator' do have magical power.