Purchase Solution

# A proof that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H

Not what you're looking for?

Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that

(Tf,f)

is real-valued for all f in H.

##### Solution Summary

It is proven that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H, where (f,f) denotes the inner product on H.
The solution is detailed and well presented.

##### Solution Preview

Recall that if T:H to H is a bounded linear operator on the Hilbert space H then there
exists a unique and bounded linear operator T^* such that

T^* : H to H

and for all g ...

##### Free BrainMass Quizzes

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts