On the nuclearity of the spaces \(S_{\Phi ({\mathcal A})}\) and \(T_{\Phi ({\mathcal A})}\). (English) Zbl 0636.46002
Summary: This paper contains manageable necessary and sufficient conditions for the nuclearity of a class of locally convex topological vector spaces which are both projective and inductive limits of Hilbert spaces.
MSC:
| 46A13 | Spaces defined by inductive or projective limits (LB, LF, etc.) |
| 46A11 | Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) |
| 46M40 | Inductive and projective limits in functional analysis |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
| 47D03 | Groups and semigroups of linear operators |
