Normed Linear Spaces Equivalent to Inner Product Spaces
نویسندگان
چکیده
منابع مشابه
Inner Products in Normed Linear Spaces
Let T be any normed linear space [l, p. S3]. Then an inner product is defined in T if to each pair of elements x and y there is associated a real number (x, y) in such a way that (#, y) » (y, x), \\x\\ = (#, #), (x, y+z) = (#,y) + (x, 2), and (/#,y) = /(#, y) for all real numbers /and elements x and y. An inner product can be defined in T if and only if any two-dimensional subspace is equivalen...
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It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.2307/2035180