0
$\begingroup$

If $A$ is a bounded linear operator on a Hilbert space such that $A$ is strictly positive. How can we prove that it has a closed Range.

$\endgroup$
3
  • $\begingroup$ Is this true? Where do you get this from? $\endgroup$ Apr 22, 2020 at 19:16
  • $\begingroup$ To prove a strictly positive bounded linear operator on a Hilbert space is invertible, I was proceeding that way. Kindly suggest any counter example if it is not true. $\endgroup$ Apr 23, 2020 at 5:42
  • $\begingroup$ Why would closed range even imply that? $\endgroup$ Apr 23, 2020 at 15:20

1 Answer 1

0
$\begingroup$

It seems your question is really about asking if every strictly positive operator is invertible. This post provides a counterexample.

$\endgroup$
1
  • $\begingroup$ Thank you for the answer. $\endgroup$ Apr 24, 2020 at 14:54

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .