The Representation Problems of Conjugate Spaces of l0(fXig) Type F-normed Spaces

WANG Jian-yong

doi:10.13371/j.cnki.chin.q.j.m.2017.03.008

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 3: 294 - 304

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.03.008

The Representation Problems of Conjugate Spaces of l⁰(fX_ig) Type F-normed Spaces

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Department of Mathematics, Changshu Institute of Technology

WANG Jian-yong(1956-), male, native of Jingning, Gansu, M.S.D., a professor of Changshu Institute of Technology, engages in functional analysis.

Online published: 2020-10-22

Supported by

Supported by the National Natural Science Foundation of China(11471236)；

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Abstract

Extending the results of an article published in(Acta Mathematica Sinica（2016,59（4）） by the author, for a sequence of normed spaces {X_i}, the representation problem of conjugate spaces of some l⁰（{X_i}） type F-normed spaces are studied in this paper. The algebraic representation continued equalities l⁰（{X_i}） * A=c₀₀⁰（{X_i}） * A= c₀₀（{X_i*}）,（l⁰（X））* A=（c⁰（X））* A=（c₀⁰（X））* A=(c₀₀⁰（X）)* A= c₀₀（X*）are obtained in the first part. Under weak-star topology, the topological representation c₀₀⁰（{X_i}） *, w* = c₀₀⁰（{X_i*}） is obtained in the second part. For the sequence of inner product spaces and number fields with the usual topology, the concrete forms of the basic representation theorems are obtained at last.

Key words： l⁰ ({X_i})type F-normed space; locally convex space; locally bounded space; conjugate space; representation theorem

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WANG Jian-yong . The Representation Problems of Conjugate Spaces of l⁰(fX_ig) Type F-normed Spaces[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(3) : 294 -304 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.03.008

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