Abstract
Letf=gt+ht be the optimal decomposition for calculating the exact value of the K-functionalK(t, f; $\bar X$ ) of an element f with respect to a couple $\bar X$ =(X0 , X1) of Banach lattices of measurable functions. It is shown that this decomposition has a rather simple form in many cases where one of the spaces X0 and X1 is either L∞ or L1. Many examples are given of couples of lattices $\bar X$ for which |gt| increases monotonically a.e. with respect to t. It is shown that this property implies a sharpened estimate from above for the Brudnyi-KrugljakK-divisibility constant γ( $\bar X$ ) for the couple. But it is also shown that certain couples $\bar X$ do not have this property. These also provide examples of couples of lattices for which γ( $\bar X$ ).
Funding Statement
Research supported by the Technion V. P. R. Fund.
Citation
Michael Cwikel. Uri Keich. "Optimal decompositions for the K-functional for a couple of Banach lattices." Ark. Mat. 39 (1) 27 - 64, March 2001. https://doi.org/10.1007/BF02388790
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