2 problems

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Local norm-attainment conjecture for Banach spaces
Local norm-attainment conjecture. If there exists a weakly open subset $U$ of $X^*$ such that
Conjectureopenbanach-spaces functional-analysis reflexivityarXiv posted 2 days ago
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The orthogonal-ideal criterion for C*-reflexivity of Hilbert C*-modules
Orthogonal-ideal criterion. The same condition should give a criterion for $C^*$ -reflexivity for general, possibly non-commutative, $C^*$ -algebras.
Conjectureopenhilbert-c-star-modules operator-algebras reflexivityarXiv posted 2 days ago

Local norm-attainment conjecture for Banach spaces