On interpolation of bilinear operators by the real method
The author studies interpolation properties of bilinear operators on Banach spaces. He obtains interesting results. One of the questions he studies is the following. Let \(F\) be an interpolation functor. It is said to interpolate bilinear operators if for arbitrary Banach pairs \(\vec X= (X_ 0,X_ 1)\), \(\vec Y= (Y_ 0,Y_ 1)\), \(\vec Z=(Z_ 0,Z_ 1)\) and for an arbitrary bilinear operator \(B: X_ i\times Y_ i\to Z_ i\) \((i=1,2)\) it follows that \(B: F(\vec X)\times F(\vec Y)\to F(\vec Z)\). Several important results are obtained for real interpolation functors.
interpolation properties of bilinear operators on Banach spaces
scientific article; zbMATH DE number 148608