Atomic Boolean Subspace Lattices and Applications to the Theory of Bases
Spiros Argyros · Michael Lambrou · William Ellison Longstaff
Jan 1991 · American Mathematical Society: Memoirs of the American Mathematical Society Book 445 · American Mathematical Soc.
Ebook
94
Pages
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About this ebook
Those families of (closed) subspaces of a (real or complex) Banach space that arise as the set of atoms of an atomic Boolean algebra subspace lattice, abbreviated ABSL, are characterized. This characterization is used to obtain new examples of ABSL's including some with one-dimensional atoms. ABSL's with one-dimensional atoms arise precisely from strong [italic capital]M-bases. The strong rank one density problem for ABSL's is discussed and some affirmative results are presented. Several new areas of investigation in the theory of ABSL's are uncovered.
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