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STABILITY OF UNCONDITIONAL SCHAUDER DECOMPOSITIONS IN
$\ell _{p}$ SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 03 August 2015, pp. 444-456
- Print publication:
- December 2015
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- Article
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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
$\ell _{p}$ 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, Chişinău, 1965), 32–44; (in Russian)] in the case of unconditional Schauder decompositions in any Banach space.
