For every countable compact K the isometry class of C(K) has its Borel complexity exactly determined, with a new characterization of L1-preduals isometric to such spaces and improved results on homeomorphism classes.
Analytic and coanalyti c families of Banach spaces, Fund
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Under analytic determinacy, σ-order bases in Banach lattices are uniform and hence Schauder, order and σ-order bases coincide, a Banach space exists with a filter Schauder basis but no ordinary one, and analytic-filter bases reduce to Borel-filter bases.
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Borel complexity of isometry classes of $\mathcal{C}(K)$ spaces with countable compacta
For every countable compact K the isometry class of C(K) has its Borel complexity exactly determined, with a new characterization of L1-preduals isometric to such spaces and improved results on homeomorphism classes.
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Coordinate systems in Banach spaces and lattices
Under analytic determinacy, σ-order bases in Banach lattices are uniform and hence Schauder, order and σ-order bases coincide, a Banach space exists with a filter Schauder basis but no ordinary one, and analytic-filter bases reduce to Borel-filter bases.