Irina Asekritova

Real interpolation of vector-valued spaces in non-diagonal case

It is shown that the formula where and is correct under the restrictions and It is also true if we suppose that and the spaces are functional Banach or quasi-Banach lattices on the same measur ...

Interpolation of Closed Subspaces and Invertibility of Operators

Let (Y0, Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj ; (j = 0; 1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (θ, q) such that the real interpolation space (X0, X1)θ, q is a closed subspace of (Y0, Y1)θ, q : In particular, we establish conditions which are necessary and sufficient for the equality (X0, X1)θ, q =(Y0, Y1)θ, q, with the proof based on a previous result by Asekritova and Kruglyak on invertibility of operators. We also generalize the theorem by Ivanov and Kalton where this problem was solved under several rather restrictive conditions, such as that X1 = Y1 and X0 is a subspace of codimension one in Y0

Interpolation of Besov spaces in the nondiagonal case

In the nondiagonal case, interpolation spaces for a collection of Besov spaces are described. The results are consequences of the fact that, whenever the convex hull of points (¯ s0 ,η 0) ,..., (¯ sn ,η n) ∈ R m+1 includes a ball of R m+1 ,w e have (l ¯0