Continuous-Like Linear Operators on Bilinear Spaces

IF 0.5 Q4 MULTIDISCIPLINARY SCIENCES

Journal of Mathematical and Fundamental Sciences Pub Date : 2020-09-08 DOI:10.5614/j.math.fund.sci.2020.52.2.8

Sabarinsyah Sabarinsyah, H. Garminia, P. Astuti

引用次数: 0

Abstract

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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双线性空间上的类连续线性算子

作为Hilbert空间上连续线性算子的推广，本文引入双线性空间上的类连续线性算子。众所周知，希尔伯特空间上线性算子伴随的存在性等价于该算子是连续的。本文将这一结果推广到双线性空间上的一类线性算子。证明了当且仅当双线性空间上的线性算子是类连续算子时，其伴随算子的存在性得到保证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical and Fundamental Sciences MULTIDISCIPLINARY SCIENCES-

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health Sciences, Medical Sciences, Pharmacy), Mathematics, Physics, and Statistics. New submissions of mathematics articles starting in January 2020 are required to focus on applied mathematics with real relevance to the field of natural sciences. Authors are invited to submit articles that have not been published previously and are not under consideration elsewhere.