For 0 〈β 〈 1, the author once wrote a paper to deal with the representation problem of the conjugate cone [L^β[0, 1]β^＊ of complex β-nanach space L^β[0, 1]. In this paper, replacing [0, 1] with a Borel finite ...For 0 〈β 〈 1, the author once wrote a paper to deal with the representation problem of the conjugate cone [L^β[0, 1]β^＊ of complex β-nanach space L^β[0, 1]. In this paper, replacing [0, 1] with a Borel finite measure space （Ω,M,μ） and replacing the complex field C with a Banach space X, we study the representation problem of the conjugate cone [L^β（μ, X）]β^＊ of L^β（μ, X）, and obtain [L^β（μ, X）]β^＊≌L^∞ M^＋（μ, S）, called the Quasi-Representation Theorem of [L^β（μ, X）]β^＊.展开更多
This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-c...This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.展开更多
This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that a...This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of aβ-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convexβ-normed space must be Chebyshev is proved at last.展开更多
基金Supported by National Natural Science Foundation of China(Grnat No.10871141)
文摘For 0 〈β 〈 1, the author once wrote a paper to deal with the representation problem of the conjugate cone [L^β[0, 1]β^＊ of complex β-nanach space L^β[0, 1]. In this paper, replacing [0, 1] with a Borel finite measure space （Ω,M,μ） and replacing the complex field C with a Banach space X, we study the representation problem of the conjugate cone [L^β（μ, X）]β^＊ of L^β（μ, X）, and obtain [L^β（μ, X）]β^＊≌L^∞ M^＋（μ, S）, called the Quasi-Representation Theorem of [L^β（μ, X）]β^＊.
文摘This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.
基金the Foundation of the Education Department of Jiangsu Province(No.05KJB110001)
文摘This paper deals with the problems of best approximation inβ-normed spaces. With the tool of conjugate cone introduced in[1]and via the Hahn-Banach extension theorem of β-subseminorm in[2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of aβ-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convexβ-normed space must be Chebyshev is proved at last.
