| 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... | |
| 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),... | |
| 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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