# zbMATH — the first resource for mathematics

On non-solid Köthe space of $$\Delta_ 2$$ type. (English) Zbl 0708.46034
In the Köthe space $$(L,\| \cdot \|_ L)$$ the author defines the functional $H(f)=\inf \{\sum^{n}_{i=1}\| \chi_{A_ i}f\|_ L:\;\| \chi_{A_ i}f\|_ L\leq 1,\quad i=1,2,...,n\},$ where the infimum is taken over all partitions $$\{A_ 1,...,A_ n\}$$. By means of the functional H one may introduce the concept of ($$\Delta$$ $${}_ 2)$$ condition to spaces of this type. The main results of the note are interesting properties of the functional H (part 2) and applications of the functional H and the $$(\Delta_ 2)$$ condition to characterize Köthe spaces (part 3).
Reviewer: A.Waszak
##### MSC:
 4.6e+31 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
##### Keywords:
Köthe space; $$(\Delta _ 2)$$ condition
Full Text: