International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 813-816
doi:10.1155/S0161171285000904
Research notes
The spaces OM and OC are ultrabornological a new proof
Department of Mathematics, Washington State University, Pullman, Washington 99164-2930, USA
Received 28 February 1985
Copyright © 1985 Jan Kucera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In [1] Laurent Schwartz introduced the spaces 𝒪M and 𝒪′C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and 𝒪′C are bornological. Our proof of this property is more constructive and based on duality.