On a Numerical Radius Preserving Onto Isometry on L(X)
We study a numerical radius preserving onto isometry on L(X). As a main result, when X is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry T on L(X) is numerical radius preserving if and only if there exists a scalar cT of modulus 1 such that...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/9183135 |
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| _version_ | 1832559772572844032 |
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| author | Sun Kwang Kim |
| author_facet | Sun Kwang Kim |
| author_sort | Sun Kwang Kim |
| collection | DOAJ |
| description | We study a numerical radius preserving onto isometry on L(X). As a main result, when X is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry T on L(X) is numerical radius preserving if and only if there exists a scalar cT of modulus 1 such that cTT is numerical range preserving. The examples of such spaces are Hilbert space and Lp spaces for 1<p<∞. |
| format | Article |
| id | doaj-art-7f52da418ee34d2cbadac49fe65ed861 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7f52da418ee34d2cbadac49fe65ed8612025-02-03T01:29:17ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/91831359183135On a Numerical Radius Preserving Onto Isometry on L(X)Sun Kwang Kim0Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of KoreaWe study a numerical radius preserving onto isometry on L(X). As a main result, when X is a complex Banach space having both uniform smoothness and uniform convexity, we show that an onto isometry T on L(X) is numerical radius preserving if and only if there exists a scalar cT of modulus 1 such that cTT is numerical range preserving. The examples of such spaces are Hilbert space and Lp spaces for 1<p<∞.http://dx.doi.org/10.1155/2016/9183135 |
| spellingShingle | Sun Kwang Kim On a Numerical Radius Preserving Onto Isometry on L(X) Journal of Function Spaces |
| title | On a Numerical Radius Preserving Onto Isometry on L(X) |
| title_full | On a Numerical Radius Preserving Onto Isometry on L(X) |
| title_fullStr | On a Numerical Radius Preserving Onto Isometry on L(X) |
| title_full_unstemmed | On a Numerical Radius Preserving Onto Isometry on L(X) |
| title_short | On a Numerical Radius Preserving Onto Isometry on L(X) |
| title_sort | on a numerical radius preserving onto isometry on l x |
| url | http://dx.doi.org/10.1155/2016/9183135 |
| work_keys_str_mv | AT sunkwangkim onanumericalradiuspreservingontoisometryonlx |