Normed Vector Spaces and Double Duals
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چکیده
In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by considering continuity. We will be more specific shortly. Let V be an R-vector space. We say that V is a normed vector space if there is a function ‖·‖ : V → R which satisfies
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Normed Vector Spaces and Double Duals
In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...
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In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...
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