Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {an*} mean the decreasing rearrangement of a sequence {|an|}. A sequence space lφ,E with symmetric (quasi)norm || {φ(n)an*} ||Ê is called ultrasymmetric, because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λφ and Mφ. We study properties of the spaces lφ,E for all admissible parameters φ, E and use them for the definition of ultrasymmetric approximation spaces Xφ,E, which essentially generalize most of classical approximation spaces. At the same time we show that the spaces Xφ,E possess almost all properties of classical prototypes, such as equivalent norms, representation, reiteration, embeddings, transformation etc. Special attention is paid to interpolation properties of these spaces. At last, we apply our results to ultrasymmetric operator ideals.
@article{urn:eudml:doc:41776,
title = {Ultrasymmetric sequence spaces in approximation theory.},
journal = {Collectanea Mathematica},
volume = {57},
year = {2006},
pages = {257-277},
zbl = {1104.41020},
mrnumber = {MR2264322},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41776}
}
Pustylnik, Evgeniy. Ultrasymmetric sequence spaces in approximation theory.. Collectanea Mathematica, Tome 57 (2006) pp. 257-277. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41776/