• Title/Summary/Keyword: A-homomorphism

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ALMOST HOMOMORPHISMS BETWEEN BANACH ALGEBRAS

  • Lee, Sung Jin;Park, Choonkil
    • Korean Journal of Mathematics
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    • v.18 no.1
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    • pp.1-10
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    • 2010
  • It is shown that for an almost algebra homomorphism between Banach algebras, there exists a unique algebra homomorphism near the almost algebra homomorphism. Moreover, we prove that for an almost algebra ${\ast}$-homomorphism between $C^{\ast}$-algebras, there exists a unique algebra ${\ast}$-homomorphism near the almost algebra ${\ast}$-homomorphism, and that for an almost algebra ${\ast}$-homomorphism between $JB^{\ast}$-algebras, there exists a unique algebra ${\ast}$-homomorphism near the almost algebra ${\ast}$-homomorphism.

SEMI-HOMOMORPHISMS OF BCK-ALGEBRAS

  • Lee, Kyoung Ja;Jun, Young Bae
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.131-139
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    • 2009
  • As a generalization of a homomorphism of BCK-algebras, the notion of a semi-homomorphism of BCK-algebras is introduced, and its characterization is given. A condition for a semi-homomorphism to be a homomorphism is provided.

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PSEUDO n-JORDAN HOMOMORPHISMS AND PSEUDO n-HOMOMORPHISMS ON BANACH ALGEBRAS

  • Ebadian, Ali;Gordji, Madjid Eshaghi;Jabbari, Ali
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.411-423
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    • 2020
  • In this paper, we correct some errors and typos of [2] and introduce a new concept related to pseudo n-Jordan homomorphisms, that we call it pseudo n-homomorphism. We investigate automatic continuity and positivity of pseudo n-homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras and C*-algebras. Moreover, we show that the sum of two pseudo n-Jordan homomorphisms is not a pseudo n-Jordan homomorphism and we show that under some conditions the sum of two pseudo n-Jordan homomorphisms is a pseudo n-Jordan homomorphism.

SOME RESULTS ON n-JORDAN HOMOMORPHISMS

  • Cheshmavar, Jahangir;Hosseini, Seyed Kamel;Park, Choonkil
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.31-35
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    • 2020
  • With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A, B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.

GENERALIZED REGULAR HOMOMORPHISM

  • Yu, Jung Ok
    • Journal of the Chungcheong Mathematical Society
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    • v.12 no.1
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    • pp.103-111
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    • 1999
  • In this paper, we introduce a generalized regular homomorphism as the extending notion of the regular homomorphism.

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ON HOMOMORPHISMS ON $C^*$-ALGEBRAS

  • Cho, Tae-Geun
    • Bulletin of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.89-93
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    • 1985
  • One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.

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