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The characterizations of the Jordan standard operator algebra isomorphism

Author: ZhaoJieLing
Tutor: ZhangJianHua
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Banach space standard operator algebra Jordan isomorphism Lie isomorphism isomorphism anti-isomorphism
CLC: O177
Type: Master's thesis
Year: 2013
Downloads: 9
Quote: 0
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Abstract


In this paper, we mainly discuss the relations between an additive or linear bijection which preserve Jordan products on the set of zero products or zero Lie products and an isomorphism or an anti-isomorphism on standard operator algebras. The details as following:In Chapter1, some notions, definitions (for example, standard operator alge-bras, Jordan isomorphism, lie isomorphism and so on) and two well-known theorems are given.In Chapter2, we mainly discuss the relations between an additive bijection which preserve Jordan products on the set of zero products or zero Lie products and an isomorphism or an anti-isomorphism, and we prove that such an additive bijection is an isomorphism or an anti-isomorphism; we also discuss the relations between additive bijection which preserve Lie products on the set of zero product and Lie isomorphism, and prove that such an additive bijection is a Lie isomorphism.In Chapter3, we mainly character every linear bijection which preserve Jordan product on the set of zero product determined on standard operator algebras, and prove that it is an isomorphism or an anti-isomorphism.

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