Let be a C*-algebra, I would like to show that is Morita equivalent to

Here follows a description of my plan to show this:

Define

let be the row matrix, then we can define the following inner products

The above choice of inner product yields the desired result which we need to have an imprimitivity bimodule, namely

I can show that in complete in the norm induced by the -inner product. But not for the norm induced by the -inner product.

I can also show that is dense in . Is it possible to show that

is dense in ?

Or is this idea totally wrong?