On isomorphic classification of tensor products $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$

Goncharov A. ; Zahariuta V. ; Terzioğlu Tosun

GDML_Books, (1996), p.

Résumé

Abstract New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$, where $E_{∞}(a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear operators into X from the dual space of the space s of rapidly decreasing sequences. Most of the results given here with proofs were announced in [12].

CONTENTS 0. Introduction...............................................5 1. Preliminaries.............................................6 2. Power series space-valued case..............8 3. Main results..............................................9 4. F- and DF-subspaces.............................11 5. Quasidiagonal isomorphism....................13 6. Sufficiency...............................................14 7. Linear Topological Invariants (LTI)..........16 8. Necessary conditions..............................20 9. Spaces $s ⊗̂ E^{\prime }_∞(b)$............................22 10. Spaces $s^{\prime } ⊗̂ E_{∞}(a)$.......................23 References.................................................26

1991 Mathematics Subject Classification: 46A04, 46A45, 46A11, 46A32.

Détail

Zbl 0852.46002

EUDML-ID : urn:eudml:doc:275828