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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Main Authors: Sabarinsyah Sabarinsyah, Hanni Garminia, Pudji Astuti
Format: Article
Language:English
Published: ITB Journal Publisher 2020-09-01
Series:Journal of Mathematical and Fundamental Sciences
Subjects:
Online Access:https://journals.itb.ac.id/index.php/jmfs/article/view/10246
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spelling 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
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