I'm asking for opinions about the 'best' notations for: 1. the algebraic dual of a vector space $X$; 2. the continuous dual of a TVS; 3. the algebraic dual (transpose) of an operator $T$ between vector spaces; 4. the dual (transpose) of a continuous operator between TVS; 5. the adjoint of a bounded operator $T$ between Hilbert spaces.

My problem is that I would like to use these notions in the same context. The standard notations tend to overlap but I am forced to use different notations for each of these entities. Of course it is easy to come up with notations, but some traditions are well established and it is not trivial to respect them and at the same time keep them apart, with some elegance.

What I'm using now: 1. $X'_{alg}$ 2. $X'$ 3. $^tT$ 4. $T'$ 5. $T^*$

Thank you for your advice.