STABILITY OF UNCONDITIONAL SCHAUDER DECOMPOSITIONS IN lp SPACES

We use the best constants in the Khintchine inequality to generalise a theorem of Kato ['Similarity for sequences of projections', Bull. Amer. Math. Soc. 73(6) (1967), 904-905] on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions in l(p) spaces. We also sharpen a stability theorem of Vizitei ['On the stability of bases of subspaces in a Banach space', in: Studies on Algebra and Mathematical Analysis, Moldova Academy of Sciences (Kartja Moldovenjaska, Chisinau, 1965), 32-44; (in Russian)] in the case of unconditional Schauder decompositions in any Banach space.