Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ be a Hilbert space. Let $T : X \rightarrow X$ be a linear mapping.

Suppose we have two scalar products $\langle\cdot,\cdot\rangle_1$ and $\langle\cdot,\cdot\rangle_2$ on $X$.

Let $T_1$ and $T_2$ the pseudoinverses of $T$ with respect to these two scalar products, respectively.

Can we estimate $\| T_1 \|$ in terms of $\| T_2 \|$?

share|cite|improve this question
I want to say no, simply because you state only that the Hilbert spaces are isomorphic. Nothing about how $S$ and $T$ are related. They would not have any other relationship even if they were in the same space. – adam W Mar 7 '13 at 19:01
Normed spaces of the same finite dimension are automatically isomorphic. // There must be some relation between $S$ and $T$, otherwise nothing can be done. The question title made me think that the linear map stays the same while the norm changes. But in the actual question no relation between $S$ and $T$ is given. – user53153 Mar 7 '13 at 19:05
I have completely rewritten the question. – shuhalo Mar 7 '13 at 19:34

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.