Lineability in subsets of measure and function spaces

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• 作者：G.A. Muñ ; oz-Ferná ; ndez ; N. Palmberg ; D. Puglisi ; J.B. Seoane-Sepú ; lveda
• 关键词：Lineability ; Spaceability ; Linear spaces ; Measure space ; Injective measure ; Function spaces
• 刊名：Linear Algebra and its Applications
• 出版年：2008
• 出版时间：1 June 2008
• 年：2008
• 卷：428
• 期：11-12
• 页码：2805-2812
• 全文大小：132 K

文摘

We show, among other results, that if λ denotes the Lebesgue measure on the Borel sets in [0,1] and X is an infinite dimensional Banach space, then the set of measures whose range is neither closed nor convex is lineable in da36aa218dfab65b6"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">ca(λ,X). We also show that, in certain situations, we have lineability of the set of X-valued and non-σ-finite measures with relatively compact range. The lineability of sets of the type L^p(I)L^q(I) is studied and some open questions are proposed. Some classical techniques together with the converse of the Lyapunov Convexity Theorem are used.