2026-06-29T02:39:07Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/346522024-07-16T15:54:55Zcom_20.500.14352_14col_20.500.14352_15

Interpolation of closed subspaces and invertibility of operators Asekritova, I. Cobos Díaz, Fernando Kruglyak, N. 51 Interpolation of subspaces K-functional Sobolev spaces Matemáticas (Matemáticas) 12 Matemáticas 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 Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T14:54:04Z 2023-06-19T14:54:04Z 2015 journal article https://hdl.handle.net/20.500.14352/34652 0232-2064 10.4171/ZAA/1525 metadata only access Heldermann Verlag