Interpolation of Closed Subspaces and Invertibility of Operators
2015 (English)In: Journal of Analysis and its Applications, ISSN 0232-2064, Vol. 34, no 2015, 1-15 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2015. Vol. 34, no 2015, 1-15 p.
Interpolation of subspaces, K-functional, Sobolev spaces.
IdentifiersURN: urn:nbn:se:liu:diva-114623DOI: 10.4171/ZAA/1525ISI: 000355126600001OAI: oai:DiVA.org:liu-114623DiVA: diva2:791511