Inner Product Spaces: Normal & Self Adjoint?

hitmeoff
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An inner product space can be both normal and self adjoint, correct?
 
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Nevermind, but I got another question, since self-adjoint means that and I.P.S. is equal to it Adjoint, wouldn't all self-adjoint I.P.S. by default be normal?
 
I have no idea what you are talking about. "Self adjoint" applies to a linear operator on an inner product space, not to the space itself.

Are you asking if "self-adjoint" and "normal" are the same for a linear operator on an inner product space?
 

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