2 problems

Conditional expectation conjecture for contractive projections on rearrangement-invariant spaces
Let $X$ be a rearrangement-invariant function space on $[0,1]$ , so that $X$ contains the constant functions, and let $P$ be a contractive projection on $X$ satisfying…
openFrom papersbanach-spaces contractive-projections rearrangement-invariant-spaces
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4
The characterization of non-strictly singular embeddings into $L_1$
Embedding conjecture. The natural embedding $E\subset L_1([0,1])$ is not strictly singular if and only if $G$ embeds continuously into $E$ .
openFrom papersbanach-spaces operator-theory rearrangement-invariant-spaces
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5

Conditional expectation conjecture for contractive projections on rearrangement-invariant spaces