Norm estimate for Moore-Penrose pseudo-inverse of $i^\ast T i$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T00:58:30Z http://mathoverflow.net/feeds/question/103590 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103590/norm-estimate-for-moore-penrose-pseudo-inverse-of-i-ast-t-i Norm estimate for Moore-Penrose pseudo-inverse of $i^\ast T i$ Martin 2012-07-31T08:15:31Z 2012-07-31T08:15:31Z <p>Let $G$ and $H$ be Hilbert spaces, let $i : G \rightarrow H$ be an isometric inclusion (so $G$ is a subspace of $H$) and let $T : H \rightarrow H$ be a bounded linear operator with closed range.</p> <p>That $T$ has closed range $R(T)$ is equivalent to the existence of a constant $C > 0$ such that</p> <p>$\forall y \in R(T) : \exists x \in T^{-1}({y}) : C \| y \|_H \geq \|x\|$</p> <p>Another equivalent condition is that the Moore-Penrose inverse of $T$, written $T^\dagger$, has a norm bounded by the constant $C$.</p> <p>Do you know a norm bound for $(i^\ast T i)^\dagger$? You assume that $G$ is finite dimensional so that $i^\ast T i$ has closed range.</p>