Accounting for several types of metric spaces, such as Gårding space, a Rienmann space, a curvilinear space, a complex Hilbert space, or others, would the criteria of self-adjointness be valid for all spaces, or can self-adjointness be violated in a different space? I.e. if an operator is self-adjoint in Hilbert space, does that then apply also for any other metric space (i.e. Gårding, Banach etc)?
This link may be useful for initial http://inmabb.criba.edu.ar/revuma/pdf/v25n1y2/p067-075.pdf
It is not really an answer to the original question but for operator T:
=
(if T is unitary or normal)
Metric spaces do not have inner products, it is usually defined for an inner product space.
Sounds good! Thanks!
But: Are there any physical properties of an operator non-self adjoint in Hilbert space, that can be derived in a Banach space? (i.e. eigenvalues etc)
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