ویراساینس.
مقاله

Embedding normed linear spaces into $C(X)$

M. Fakhar, M. R. Koushesh, M. Raoofi

چکیده

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 indeed be chosen to be the Stone--Cech compactification of $L^*\setminus\{0\}$, where $L^*\setminus\{0\}$ is endowed with the supremum norm topology.

اسناد مشابه

  • embedding normed linear spaces into $c(x)$

    مقالهbulletin of the iranian mathematical societym. fakhar, department of mathematics‎, ‎university of isfahan‎, ‎isfahan 81745--163‎, ‎iran‎, ‎and‎, ‎school of mathematics‎, ‎institute for research in fundamental sciences (ipm)‎, ‎p.o‎. ‎box: ‎19395--5746‎, ‎tehran‎, ‎iran. m. r. koushesh, department of mathematical sciences‎, ‎isfahan university of technology‎, ‎isfahan 84156--83111‎, ‎iran‎, ‎and‎, ‎school of mathematics‎, ‎institute for research in fundamental sciences (ipm)‎, ‎p.o‎. ‎box‎: ‎19395--5746‎, ‎tehran‎, ‎iran. m. raoofi, department of mathematical sciences‎, ‎isfahan university of technology‎, ‎isfahan 84156--83111‎, ‎iran.

    ‎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$

  • The Finite Dimensional Normed Linear Space Theorem

    سند علمی۲۰۱۲Richard DiSalvo

    The claim that follows, which I have called the nite-dimensional normed linear space theorem, essentially says that all such spaces are topologically R with the Euclidean norm. This means that in many cases the intuition we obtain in R,R, and R by imagining intervals, circles, an

  • Inner Products in Normed Linear Spaces

    سند علمی۲۰۰۷ROBERT C. JAMES

    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

  • a new perspective to the mazur-ulam problem in $2$-fuzzy $2$-normed linear spaces

    مقاله۲۰۱۰iranian journal of fuzzy systemscihangir alaca

    in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed lin

  • A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces

    مقاله۲۰۱۰Iranian Journal of Fuzzy SystemsCihangir Alaca

    In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed lin

  • gradual normed linear space

    مقاله۲۰۱۱iranian journal of fuzzy systemsi. sadeqi, f. y. azari

    in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so t