| Title:
|
Extensions of linear operators from hyperplanes of $l^{(n)}_\infty$ (English) |
| Author:
|
Baronti, Marco |
| Author:
|
Fragnelli, Vito |
| Author:
|
Lewicki, Grzegorz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
443-458 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| 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 |
| idZBL:
|
Zbl 0831.41014 |
| idMR:
|
MR1364484 |
| . |
| Date available:
|
2009-01-08T18:19:11Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118772 |
| . |
| 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 |
| . |
