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" The set of all linear continuous functionals on X is called the adjoint or conjugate space of X and is denoted X*. "
Nonsmooth Variational Problems and Their Inequalities: Comparison Principles ... - Page 15
by Siegfried Carl, Vy Khoi Le, Dumitru Motreanu - 2007 - 398 pages
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Mathematical Models in Electrical Circuits: Theory and Applications

C. A. Marinov, Pekka Neittaanmäki - Technology & Engineering - 1991 - 186 pages
...5(x,r) = 8B(x,r) = {y 6 X ; ||y - x|| = r} and B(x,r) = B(x,r) US(i,r) respectively. The space .Y* of all linear continuous functionals on X is called the dual space of X. The space X* is also Banach with respect to the norm ||/||= sup {|/(*)|; H<1}. Beside the strong...
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Applied Functional Analysis: Applications to Mathematical Physics

Eberhard Zeidler - Mathematics - 1999 - 526 pages
...normed space over K. By a linear continuous functional on A' we understand a linear continuous operator The set of all linear continuous functionals on X is called the dual space X* ofX. Obviously, X* = L(A',K). We set (/.u):=/(u) for all u €x. / € A*. Let / € X* . By (67),...
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Mesh Enhancement: Selected Elliptic Methods, Foundations and Applications

Glen A. Hansen, R. W. Douglass, Andrew Zardecki - Science - 2005 - 534 pages
...that / is a continuous map. Conversely, a continuous linear functional is bounded [Zeidler, 1995]. The set of all linear continuous functionals on X is called the dual space X* of X. An example of the functional in L-^^l) is provided by the integral l(u) = I v(x)u(x) dx. (3.32) Jet...
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