- #1
SeM
Hi, I have an operator which does not obey the following condition for boundedness:
\begin{equation*}
||H\ x|| \leqslant c||x||\ \ \ \ \ \ \ \ c \in \mathscr{D}
\end{equation*}
where c is a real number in the Domain D of the operator H.
However, this operator is also not really unbounded, because if H was unbounded, it would give an incorrect inequality, examplewise: if an bounded operator gives a valid inequality (i.e x < cx), a unbounded operator gives an invalid inequality (i.e x > cx). This operator however gives a result with complex values!
What can one say about its bounded/unbounded state then?
Thanks!
\begin{equation*}
||H\ x|| \leqslant c||x||\ \ \ \ \ \ \ \ c \in \mathscr{D}
\end{equation*}
where c is a real number in the Domain D of the operator H.
However, this operator is also not really unbounded, because if H was unbounded, it would give an incorrect inequality, examplewise: if an bounded operator gives a valid inequality (i.e x < cx), a unbounded operator gives an invalid inequality (i.e x > cx). This operator however gives a result with complex values!
What can one say about its bounded/unbounded state then?
Thanks!