The uncertainty operator and Heisenberg

[dyn]

In deriving the Heisenberg uncertainty relation for 2 general Hermitian operators A and B , the uncertainty operators ΔA and ΔB are introduced defined by ΔA=A - (expectation value of A) and similarly for B.
My question is this - how can you subtract(or add) an expectation value , which is just a number to A which is an operator ?

 

[atyy]

A number is also an operator. But you can also see it by the variance being <A.A>-<A>², where <A.A> is a number and <A> is a number.

<(A-<A>)²>
= <A.A-2<A>A+<A>²>
= <A.A>-<2<A>A>+<<A>²>
= <A.A>-2<A><A>+<<A>²>
= <A.A>-<A>²

 

[WannabeNewton]

There's an implicit identity operator multiplying $\langle A \rangle$.

 

[dextercioby]

That's sloppy and indeed misleading notation. The unit operator on the states' space is not written when scaled by the expectation value.