MathOverflow is a question and answer site for professional mathematicians. 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

Can someone give me an example of a Banach space $X$ and contractive projection $P\in\mathcal{B}(X)$ such that $\ker P$ is not a range of any contractive projection $Q\in\mathcal{B}(X)$?

share|cite|improve this question
up vote 2 down vote accepted

The projection from the space $c$ of convergent sequences to the $1$-dimensional subspace of constant sequences with kernel $c_0$. Any projection $c \to c_0$ has norm at least $2$ (cf. exercises to chapter 2.5 in Albiac-Kalton).

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.