Let T be a positive compact operator on a Hilbert space then we know that an operator equation $X^2 = T$ have a solution.
Im confused since we have a result which says that a compact operator $T \geq 0$ have an unique operator $X$ which is compact, positive and $X^2 = T$. How there can be a compact operator $T\geq 0$ which have uncountable many solutions?
The result where im refering, its from John B. Conway, A course in functional analysis, Graduate Texts in Mathematics 96, Springer 1990.: 
What would be an example of an operator $T$ which have uncountable many solutions?