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Research on Additive Mapping Preserving Anti-orthogonality and Preserving Commutative Zero-product

Author: ZhangFangJuan
Tutor: JiGuoXing
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Paul the inverse orthogonal Paul Jordan orthogonality Preserving Orthogonality Idempotent operator Paul exchange zero plot Additive Maps
CLC: O177
Type: Master's thesis
Year: 2006
Downloads: 35
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Abstract


Operator Algebras maintained PRESERVING is to study some characteristics of the same algebra mapping. The results show that, in many cases, this mapping is the algebra homomorphism or algebra anti-homomorphism. Which reveals the inherent nature of operator algebra and its mapped on the link, so that people further deepen the awareness and understanding of the operator algebra. The results of their research not only enriches the operator algebra and functional analysis of the conclusions of the original, and its practical value in the system theory and quantum mechanics. B (X) as the basic operator algebra, to maintain the issue of research is to the other operator algebra maintain research. This is Paul B (X) Anyway, cross-resistance additive maps and insurance exchange Zero - product additive maps were studied, the following results: 1 depicts the B (H) to B (K) Paul inverse orthogonal sex, Paul Jordan orthogonal additive mapping B (H) and B (K) is the Banach algebra of all bounded operator on a Hilbert space H and K. Phi: B (H) - → B (K) is a bilateral Paul inverse orthogonal and can be added surjective, making Phi (I) = I, and for each rank one idempotent operator P ∈ B (H) The Phi (FP) (?) FΦ (P). Φ B (H) * - anti-isomorphic or conjugated * - anti-isomorphic. Paul anyway post the same assumptions, For Paul Jordan orthogonality get Phi is one of the following forms: * - isomorphic conjugate * - isomorphic * - anti-isomorphic conjugate * - anti-isomorphic . Study B (H) preserving additive maps exchange zero plot, where B (H) is a Banach algebra of all bounded operator on the Hilbert space H. Firstly, in the finite-dimensional case, if Φ insurance exchange zero plot can be added surjective, making Phi (I) = I, and for each rank one idempotent operator P of ∈ M_n has Phi (FP) (?) FΦ (P) Φ is an automorphism or anti-automorphism. Further given the infinite-dimensional case, if Φ insurance exchange zero plot can be added surjective, then Φ is isomorphic non-zero number multiplied by a ring or a ring anti-isomorphic. Discussion of A, B preserving exchange Zero - product additive maps, where A, B Banach space X standard operator algebra. Assume that Φ: A-→ B is a security units can be added surjective. Φ insurance exchange product and phi (FP) on all rank one idempotent operator P ∈ A (?) FΦ (P) and Phi (P) = 0 holds. Φ one of the following four forms: algebra isomorphic conjugate algebra is isomorphic to the algebra anti-isomorphic conjugate algebra anti-isomorphic.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis
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