Operators are not immutable. Operator properties are dynamic and among other things affect equality!
(1) -> f:=operator 'f
g:=operator 'f
test(f=g)
test(kernels f(x) = kernels g(x))
test(f(x)=g(x))
name f
name g
Change or add a property.
display(g,(x:List OutputForm):OutputForm+->prefix('G, x)$OutputForm)
g(x)
test(f=g)
test(kernels f(x) = kernels g(x))
test(f(x)=g(x))
name f
name g