Formulae for the distance in some quasi-Banach spaces |
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| Authors: | David E. Edmunds Georgi E. Karadzhov |
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| Affiliation: | (1) Department of Mathematics, University of Sussex, BN1 9RF Brighton, UK;(2) Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, BG-1113 Sofia, Bulgaria |
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| Abstract: | Let (A 0, A 1 ) be a compatible pair of quasi-Banach spaces and 1etA be a corresponding space of real interpolation type such thatA 0 ∩A 1 is not dense inA. Upper and lower estimates are obtained for the distance of any elementf ofA fromA 0 ∩A 1 . These lead to formulae for the distance in a large number of concrete situations, such as whenA 0 ∩A 1 =L ∞ andA is either weak-L q, a ‘grand’ Lebesgue space or an Orlicz space of exponential type. |
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