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- Homework Statement
- Prove properties of unitary operator

- Relevant Equations
- Unitary maps are bijective and have the property of <Af,Ag>=<f,g>

Hello folks,

I need to show that a unitary operator obeys <Af,Ag>=<f,g>, where A is a unitary operator. However, I am technically not yet given the fact, that the adjoint of A is equal to its inverse, and that is the problem. I have no clue how to prove the given task without using the mentioned statement.

The space the scalaroduct is defined in is the $L^2$ space.

I need to show that a unitary operator obeys <Af,Ag>=<f,g>, where A is a unitary operator. However, I am technically not yet given the fact, that the adjoint of A is equal to its inverse, and that is the problem. I have no clue how to prove the given task without using the mentioned statement.

The space the scalaroduct is defined in is the $L^2$ space.