Continuous-Like Linear Operators on Bilinear Spaces | Zendy

Sabarinsyah Sabarinsyah | Zendy; Hanni Garminia | Zendy; Pudji Astuti | Zendy

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Continuous-Like Linear Operators on Bilinear Spaces

Author(s) -

Sabarinsyah Sabarinsyah,

Hanni Garminia,

Pudji Astuti

Publication year - 2020

Publication title -

journal of mathematical and fundamental sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.216

H-Index - 12

eISSN - 2337-5760

pISSN - 2338-5510

DOI - 10.5614/j.math.fund.sci.2020.52.2.8

Subject(s) - mathematics , continuous linear operator , bilinear interpolation , hilbert space , nuclear operator , operator (biology) , hermitian adjoint , operator theory , linear map , generalization , finite rank operator , bilinear map , compact operator on hilbert space , multiplication operator , mathematical analysis , quasinormal operator , compact operator , pure mathematics , computer science , banach space , transcription factor , extension (predicate logic) , biochemistry , statistics , chemistry , repressor , gene , programming language

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.

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