Weakly Sequential Completeness of Hilbert Spaces
DAI Bing
YAN Yan
BAO Yu′e
Abstract：In this paper,we introduce a concept of the weak convergence in the inner product space, and research the problem about the weak sequential completeness of Hilbert space.Firstly,we introduce a con-cept of weak convergence of a sequence in the inner product space,which is called the weak convergence in inner product space.And we discuss the property of weak convergent sequence in inner product space. The properties like the uniqueness of the weakly sequental convergent point in inner product space and the boudedness of weak convergent inner product sequence are proved. Secondly,we introduce the con-cepts of basic weak sequence and weakly sequential completeness,and prove that the Hilbert space is a space whose sequence is weakly complete.
Keywords：inner product spaceHilbert spaceweak inner product convergenceweak basic sequenceweak sequential completeness
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：6( 380-385 )