Abstract
We characterize 1-complemented subspaces of finite codimension in strictly monotone one-p-convex, 2 < p < ∞, sequence spaces. Next we describe, up to isometric isomorphism, all possible types of 1-unconditional structures in sequence spaces with few surjective isometries. We also give a new example of a class of real sequence spaces with few surjective isometries.
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