Let $J$ be the James space. I have the following questions:

Question 1: Does every infinite-dimensional closed subspace of $J$ contain an infinite-dimensional closed subspace that is $C$-complemented in $J$? where the $C$ is the universal constant.

Question 2: Let $(u_{n})_{n}$ be a normalized skipped block basic sequence of the unit vector basis in $J$. Is the subspace spanned by $(u_{n})_{n}$ $C$-complemented in $J$? where the $C$ is the universal constant.

Obviously, if Question 2 is true, then Question 1 is true. I do not know what is the above universal constant $C$.

Thank you!

yes. See the comments after Remark 2.11 in arxiv.org/abs/1401.4231 and Proposition 2.4 in acadsci.fi/mathematica/Vol36/… I do not know the answer to question 2. $\endgroup$ – Ben W Jul 10 '16 at 23:53The James Forestby Helga Fetter and Berta Gamboa de Buen. Most of it is on Google books. books.google.com/books?id=GQJVVtDwx5wC&pg=PA43 $\endgroup$ – Ben W Jul 11 '16 at 0:23