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Lower bounds for the norms of projections with small kernels

Published online by Cambridge University Press:  17 April 2009

Carlo Franchetti
Carlo Franchetti
Affiliation:
Dipartimento di Matematica Applicata “G. Sansone”Universita degli Studi di Firenze via S. Marta 3 50139 Firenze, Italy
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Abstract

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Popov has recently introduced a class of subspaces of Lp(μ) (μ nonatomic) which generalise the finite codimensional ones, and proved that for p ≠ 2 any projection onto such a subspace has a norm strictly greater than one. In this paper we give the quantitative version of Popov's result computing the best possible lower bound for the norms of the considered projections.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 507 - 511
Copyright
Copyright © Australian Mathematical Society 1992

References

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