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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 813-816
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 Hindawi Publishing Corporation. 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.


In [1] Laurent Schwartz introduced the spaces 𝒪M and 𝒪C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both 𝒪M and 𝒪C are bornological. Our proof of this property is more constructive and based on duality.