1

In this answer the author mentions the concept of $1$-complementability as an example of a property of Banach spaces that is not preserved under (non-isometric) isomorphisms.

I couldn't find any information about this notion anywhere.

Carla_
  • 361

1 Answers1

1

We say that a closed subspace $Y$ of a Banach space is $\lambda$-complemented, if there exists a linear projection $P:X\to Y$ with $\|P\| \leq \lambda$. In particular, it's $1$-complemented if there exists a projection onto $Y$ of norm $1$.

Reference: Definition 4.1 in Banach Space Theory: The basis for linear and nonlinear analysis by Fabian, Habala, Hájek, Montesinos and Zizler

Jakobian
  • 15,280