Orthogonality preserving mappings on inner product C*-modules

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Khalili Gholi Abad Ali; Amyari Maryam

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ISSN: 2588-4824

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2019 | Volume:5 | Issue:20 Page(s): 49-56

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Title

Orthogonality preserving mappings on inner product C*-modules

Author(s)

Khalili Gholi Abad Ali | Amyari Maryam | Issue Writer Certificate

Keywords

orthogonality

orthogonality preserving mapping

inner product A-module space

Abstract

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 of all positive elements of A. We show that an A-linear mapping T: E→ F preserves orthogonality if and only if there exists a∈ A+ such that ⟨ Tx, Ty⟩ = a^2 ⟨ x, y⟩ for each x, y∈ E. At first recall that two vector x, y∈ E are ordinary orthogonal if ⟨ x, y⟩ =0 and then we introduce the notion of orthogonality in an inner product A-module in three ways and show that an A-linear mapping between two inner product A-modules preserves the ordinary orthogonality if and only if it preserves each one of the new orthogonality.

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APA: Copy

Khalili Gholi Abad, Ali, & Amyari, Maryam. (2019). Orthogonality preserving mappings on inner product C*-modules. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(20 ), 49-56. SID. https://sid.ir/paper/741293/en

Vancouver: Copy

Khalili Gholi Abad Ali, Amyari Maryam. Orthogonality preserving mappings on inner product C*-modules. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2019;5(20 ):49-56. Available from: https://sid.ir/paper/741293/en

IEEE: Copy

Ali Khalili Gholi Abad, and Maryam Amyari, “Orthogonality preserving mappings on inner product C*-modules,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 20 , pp. 49–56, 2019, [Online]. Available: https://sid.ir/paper/741293/en

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