Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 2 / 17F / i

Table of contents
- Solution i

Solution

A normal operator satisfies

α^{*} α = α α^{*}

. Moving an operator across the inner product gives

∥ αv ∥^{2} = ⟨ v, α^{*} αv ⟩ = ⟨ v, α α^{*} v ⟩ = ∥ α^{*} v ∥^{2} .

One of these norms is zero exactly when the other is zero. Therefore

ker α = ker α^{*} .

 Ancestors (10)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version