Stability of the orthogonality preserving property in finite-dimensional inner product spaces
نویسندگان
چکیده
منابع مشابه
Orthogonality preserving mappings on inner product C* -modules
Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...
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Definition 1. An inner product on a complex vector space V is a map 〈., .〉 : V × V → C such that (i) 〈., .〉 is linear in the first slot: 〈c1v1 + c2v2, w〉 = c1〈v1, w〉+ c2〈v2, w〉, c1, c2 ∈ C, v1, v2, w ∈ V, (ii) 〈., .〉 is Hermitian symmetric: 〈v, w〉 = 〈w, v〉, with the bar denoting complex conjugate, (iii) 〈., .〉 is positive definite: v ∈ V ⇒ 〈v, v〉 ≥ 0, and 〈v, v〉 = 0⇔ v = 0. A vector space with ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.06.016