It is difficult for me to explain the background of this question, but I would like to know the following statement is true or not:
Let $H$ be a Hilbert space, and let $A, B \in B(H)$ be self-adjoint and non-negative. Then, $(A+B)^s \leq A^s + B^s$ for any $s \in [0, 1]$.
Lately, I have often encountered such kind of operator inequalities. There are many papers that deal with this type of issue, but I don't know any good textbook. I would appreciate it if you could point me to an appropriate textbook.