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On the representation of norm attaining positive operators on $$L^ p[0,1]$$. (English) Zbl 0545.47018
Let $$1<r\leq p<\infty$$. In this paper an integral representation of positive operators from the set $${\mathcal N}=\{T\in {\mathcal L}(L^ p[0,1],L^ r[0,1]):\quad there\quad exists\quad f\in L^ p[0,1]\quad such\quad that\quad \| Tf\| =\| f\| \| T\| \quad and\quad \sup p f=[0,1]\}$$ is given. To obtain the above result Ryff’s representation theorem of doubly stochastic operators is used.
##### MSC:
 47B38 Linear operators on function spaces (general)