In the memoir we examine the question which Banach spaces have a unique unconditional basis, up to equivalence and permutation. We solve this question for some infinite direct sums of classical sequence spaces and for a Tsirelson type space. We also classify, up to isomorphism, …
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-dime…