Continuous-Like Linear Operators on Bilinear Spaces
This paper introduces continuous-like linear operators on bilinear spaces as a generalization of continuous linear operators on Hilbert spaces. It is well known that the existence of the adjoint of a linear operator on a Hilbert space is equivalent to the operator being continuous. In this paper, th...
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doaj-02a1fc7f632e409ba57c9e67638d40a32021-07-10T06:06:48ZengITB Journal PublisherJournal of Mathematical and Fundamental Sciences2337-57602338-55102020-09-0152210.5614/j.math.fund.sci.2020.52.2.8Continuous-Like Linear Operators on Bilinear SpacesSabarinsyah Sabarinsyah0Hanni Garminia1Pudji Astuti2Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Ganesha No. 10 Bandung 40132Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Ganesha No. 10 Bandung 40132Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Ganesha No. 10 Bandung 40132This paper introduces continuous-like linear operators on bilinear spaces as a generalization of continuous linear operators on Hilbert spaces. It is well known that the existence of the adjoint of a linear operator on a Hilbert space is equivalent to the operator being continuous. In this paper, this result is extended to the class of linear operators on bilinear spaces. It is shown that the existence of the adjoint of a linear operator on a bilinear space is guaranteed if and only if the operator is continuous-like.https://journals.itb.ac.id/index.php/jmfs/article/view/10246adjoint operatorsbilinear spacesclosed subspacescontinuouscontinuous-likeHilbert spaces |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sabarinsyah Sabarinsyah Hanni Garminia Pudji Astuti |
spellingShingle |
Sabarinsyah Sabarinsyah Hanni Garminia Pudji Astuti Continuous-Like Linear Operators on Bilinear Spaces Journal of Mathematical and Fundamental Sciences adjoint operators bilinear spaces closed subspaces continuous continuous-like Hilbert spaces |
author_facet |
Sabarinsyah Sabarinsyah Hanni Garminia Pudji Astuti |
author_sort |
Sabarinsyah Sabarinsyah |
title |
Continuous-Like Linear Operators on Bilinear Spaces |
title_short |
Continuous-Like Linear Operators on Bilinear Spaces |
title_full |
Continuous-Like Linear Operators on Bilinear Spaces |
title_fullStr |
Continuous-Like Linear Operators on Bilinear Spaces |
title_full_unstemmed |
Continuous-Like Linear Operators on Bilinear Spaces |
title_sort |
continuous-like linear operators on bilinear spaces |
publisher |
ITB Journal Publisher |
series |
Journal of Mathematical and Fundamental Sciences |
issn |
2337-5760 2338-5510 |
publishDate |
2020-09-01 |
description |
This paper introduces continuous-like linear operators on bilinear spaces as a generalization of continuous linear operators on Hilbert spaces. It is well known that the existence of the adjoint of a linear operator on a Hilbert space is equivalent to the operator being continuous. In this paper, this result is extended to the class of linear operators on bilinear spaces. It is shown that the existence of the adjoint of a linear operator on a bilinear space is guaranteed if and only if the operator is continuous-like. |
topic |
adjoint operators bilinear spaces closed subspaces continuous continuous-like Hilbert spaces |
url |
https://journals.itb.ac.id/index.php/jmfs/article/view/10246 |
work_keys_str_mv |
AT sabarinsyahsabarinsyah continuouslikelinearoperatorsonbilinearspaces AT hannigarminia continuouslikelinearoperatorsonbilinearspaces AT pudjiastuti continuouslikelinearoperatorsonbilinearspaces |
_version_ |
1721309884526362624 |