Operator Equations: Add, Subtract, Multiply & Divide

[mpkannan]

A mathematical operator (Aop) operates on a function (f) to generate a new function (f '):
Aop (f) = f ' (1)

Consider that I subtract a from b to get c:
b-a = c (2)

Can I write this subtraction operation as an operator equation of the form (1) as shown below?

(-a) (b) = c (3)

where (-a) represents the operator "subtract a".

Similarly for +, x and /.

 

[MathematicalPhysicist]

Yes, you can be it won't be a linear operator like taking a derivative (if that's what ' represents), at the most it's an affine function.

 

[JSuarez]

You can write either as:

1) A bilinear operator, that is, one that takes as inputs pairs of arguments: A(a,b)=a-b. In this case, your -a is A(a,...).

2) Directly, like you propose, but then you have a family of operators, one for each a, or an affine operator, for a fixed a.