2 problems

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Near-triviality conjecture for isometries of complex HI spaces
Let $X$ be a complex HI space, meaning a hereditarily indecomposable Banach space, and let the group of isometries of $X$ act on $X$ . Near-triviality conjecture. The group of isome…
Conjecturerefutedbanach-spaces hereditarily-indecomposable-spaces isometry-groupsarXiv posted 2 days ago
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The conjecture that the Gowers–Maurey space is of type (1)
Gowers–Maurey type (1) conjecture. The Gowers–Maurey space is of type (1).
Conjectureopenbanach-spaces hereditarily-indecomposable-spacesarXiv posted 2 days ago

Near-triviality conjecture for isometries of complex HI spaces