Math Forum :: View topic – Linear Algebra

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Jonathanlam

Joined: 26 Jan 2004Posts: 14

Location: Hong Kong

Posted: Tue Jan 27, 2004 6:05 pm    Post subject: Linear Algebra

Let a,b be endomorphism of a linear space X.Prove that if X is finite-dimensional then ab-ba not equals the identity map.Thanks.

aRdolf

Frequent VisitorJoined: 18 Jan 2004Posts: 37

Posted: Tue Jan 27, 2004 8:25 pm    Post subject:

Let A, B be invertible matrices,
then tr(AB-BA)=trAB-trBA=trAB-trAB=0, not equal to n=dimension.

aRdolf

Frequent VisitorJoined: 18 Jan 2004Posts: 37

Posted: Tue Sep 14, 2004 11:28 am    Post subject:

I wonder if this result is true for infinite dimensional spaces. The trace works well for trace class operators in Hilbert Space.

How about arbitrary endomorphisms on Banach Spaces?

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