For hypothesis A\supseteq B so \mathcal{D}_A\supseteq\mathcal{D}_B and A\mathbf{x}=B\mathbf{x}\,\,\forall\,\mathbf{x}\in \mathcal{D}_B. Let \mathbf{a}\in\mathcal{D}_A then A\mathbf{a}+\imath \mathbf{a}\in\mathcal{H}. For hypothesis \mathcal{R}_{A+\imath I}=\mathcal{R}_{B+\imath I}, so...
A functional analysis' problem
I hope this is the right place to submit this post.
Homework Statement
Let A be a symmetric operator, A\supseteq B and \mathcal{R}_{A+\imath I}=\mathcal{R}_{B+\imath I} (where \mathcal{R} means the range of the operator). Show that A=B.
2. The attempt at a...