The spaces <mml:math alttext="$O_M $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>O</mml:mi><mml:mi>M</mml:mi></mml:msub></mml:math> and <mml:math alttext="$O_C $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>O</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math> are ultrabornological a new proof

Kucera, Jan

doi:https://doi.org/10.1155/S0161171285000904

International Journal of Mathematics and Mathematical Sciences

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Research notes | Open Access

Volume 8 | Article ID 924289 | https://doi.org/10.1155/S0161171285000904

The spaces OM and OC are ultrabornological a new proof

Jan Kucera¹

Received28 Feb 1985

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.

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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.

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