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On interpolation of bilinear operators by the real method. (English. Russian original) Zbl 0798.46054
Math. Notes 52, No. 1, 641-648 (1992); translation from Mat. Zametki 52, No. 1, 15-24 (1992).
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.

46M35 Abstract interpolation of topological vector spaces
46B70 Interpolation between normed linear spaces
Full Text: DOI
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