Equimodular and linearity in modular spaces |
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Authors: | Jian Wang Jian-Yong Wang |
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Institution: | a Department of Mathematics, Nanjing University, Nanjing 210093, China b Department of Mathematics, Fujian Normal University, Fuzhou 350007, China c Department of Mathematics, Changshu College, Jiangsu 215500, China |
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Abstract: | In this paper, the concept of equimodular is introduced. It contains several generalizations of Mazur-Ulam's isometric theorem in modular spaces. Let X and Y be two real modular spaces and X with δ1-midpoint shrinking whose modular ρX satisfies the Δ2-condition. Assume that an operator T maps X onto Y in an δ2-{ti}-equimodular manner for all , where {ti} is a null-sequence of nonnegative reals with the property that t0=1, t1?1/2, and ti?ti−1?2ti for i?2. Then T is affine. |
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Keywords: | Equimodular δ-t-equimodular δ-midpoint shrinking Inverting modular Parental modular |
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