## Product unbounded operators

Let $A : D(A) subset H rightarrow H$ be unbounded and $B$ be a bounded operator, both of them are self-adjoint, then $(AB)^* = B^*A^*$ and $(BA)^* = A^*B^*$, right? I just wanted to be sure that …

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If $X$ $Y$ are Banach space, $T$ is a linear operator between them. I don’t understand the following statement: If $T$ is not continuous, then for each $nin N$, there exists $x_nin X$ such that $$|…

The following is a question I came up with when I was studying the same problem in dimension 1 (for which also I have the questions that follows) but I put in generality. Let $U_1, U_2 subset …