Say we have an n-dimensional row vector with entries in a C*-algebra . We construct the matrix
How do we show that this matrix is positive?
Here is my idea:
If we have a representation for some Hilbert space , we can inflate this homomorphism to
with norm which makes into a C*-algebra.
Furthermore we know that is isomorphic to where .
We know that , so it is self adjoint. Now is we can show that where then the matrix is positive.
So
so when we have positivity, but what about the terms where ?
Or am I completely on the wrong track?