Approximately orthogonality preserving mappings on C^*-modules

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• 作者：Dijana Iliš ; ević ; ; Aleksej Turnš ; ek
• 关键词：Hilbert ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4PYYV23-1&_mathId=mml21&_user=10&_cdi=6894&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=452d6873d5ec46919244c252fa2f0c88
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 May 2008
• 年：2008
• 卷：341
• 期：1
• 页码：298-308
• 全文大小：158 K

文摘

We study orthogonality preserving and approximately orthogonality preserving mappings in the setting of inner product C^*-modules. In particular, if V and W are inner product C^*-modules over the C^*-algebra , any scalar multiple of an -linear isometry is an -linear orthogonality preserving mapping. The converse does not hold in general, but it holds if contains (the C^*-algebra of all compact operators on a Hilbert space ). Furthermore, we give the estimate of Tx,Ty−T²x,y for an -linear approximately orthogonality preserving mapping T:V→W when V and W are inner product C^*-modules over a C^*-algebra containing . In the case and V, W are Hilbert, we also prove that an -linear approximately orthogonality preserving mapping can be approximated by an 72392e23e193"">-linear orthogonality preserving mapping.