Continuous-Like Linear Operators on Bilinear Spaces

被引：0

作者：

Sabarinsyah ^{[1
]}

Garminia, Hanni ^{[1
]}

Astuti, Pudji ^{[1
]}

机构：

[1] Inst Teknol Bandung, Fac Math & Nat Sci, Algebra Res Grp, Ganesha 10, Bandung 40132, Indonesia

来源：

JOURNAL OF MATHEMATICAL AND FUNDAMENTAL SCIENCES | 2020年 / 52卷 / 02期

关键词：

adjoint operators; bilinear spaces; closed subspaces; continuous; continuous-like; Hilbert spaces;

D O I：

10.5614/j.math.fund.sci.2020.52.x.x

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：250 / 258

页数：9

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