Academic Journal
Extensions of linear operators from hyperplanes of $l^{(n)}_\infty$
| العنوان: | Extensions of linear operators from hyperplanes of $l^{(n)}_\infty$ |
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| المؤلفون: | Baronti, Marco, Fragnelli, Vito, Lewicki, Grzegorz |
| بيانات النشر: | Charles University in Prague, Faculty of Mathematics and Physics |
| سنة النشر: | 1995 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:linear operator, keyword:extension of minimal norm, keyword:element of best approximation, keyword:strongly unique best approximation, msc:41A35, msc:41A52, msc:41A55, msc:41A65, msc:46A22, msc:47A20 |
| الوصف: | summary:Let $Y \subset l^{(n)}_{\infty }$ be a hyperplane and let $A \in {\Cal L}(Y)$ be given. Denote $$ \align {\Cal A} = & \{L\in {\Cal L}(l^{(n)}_{\infty },Y):L\mid Y = A\} \text{ and} \ & \lambda_{A} = \inf \{\parallel L \parallel : L\in {\Cal A}\}. \endalign $$ In this paper the problem of calculating of the constant $\lambda_{A}$ is studied. We present a complete characterization of those $A \in {\Cal L}(Y)$ for which $\lambda_{A} = \parallel A \parallel $. Next we consider the case $\lambda_{A} > \parallel A \parallel $. Finally some computer examples will be presented. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0010-2628 1213-7243 |
| Relation: | mr:MR1364484; zbl:Zbl 0831.41014; reference:[1] Baronti M., Papini P.L.: Norm one projections onto subspaces of $l^p$.Ann. Mat. Pura Appl. IV (1988), 53-61. MR 0980971; reference:[2] Blatter J., Cheney E.W.: Minimal projections onto hyperplanes in sequence spaces.Ann. Mat. Pura Appl. 101 (1974), 215-227. MR 0358179; reference:[3] Collins H.S., Ruess W.: Weak compactness in spaces of compact operators and vector valued functions.Pacific J. Math. 106 (1983), 45-71. MR 0694671; reference:[4] Odyniec Wl., Lewicki G.: Minimal Projections in Banach Spaces.Lecture Notes in Math. 1449, Springer-Verlag. Zbl 1062.46500, MR 1079547; reference:[5] Singer I.: On the extension of continuous linear functionals.Math. Ann. 159 (1965), 344-355. Zbl 0141.12002, MR 0188758; reference:[6] Singer I.: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces.Springer-Verlag, Berlin, Heidelberg, New York, 1970. Zbl 0197.38601, MR 0270044; reference:[7] Sudolski J., Wojcik A.: Some remarks on strong uniqueness of best approximation.Approximation Theory and its Applications 6 (1990), 44-78. Zbl 0704.41016, MR 1078687 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/118772 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.7EC7AC21 |
| قاعدة البيانات: | BASE |
| تدمد: | 00102628 12137243 |
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