• Title/Summary/Keyword: Injective norm

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Injective JW-algebras

  • Jamjoom, Fatmah Backer
    • Kyungpook Mathematical Journal
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    • v.47 no.2
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    • pp.267-276
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    • 2007
  • Injective JW-algebras are defined and are characterized by the existence of projections of norm 1 onto them. The relationship between the injectivity of a JW-algebra and the injectivity of its universal enveloping von Neumann algebra is established. The Jordan analgue of Theorem 3 of [3] is proved, that is, a JC-algebra A is nuclear if and only if its second dual $A^{**}$ is injective.

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The Structure of Maximal Ideal Space of Certain Banach Algebras of Vector-valued Functions

  • Shokri, Abbas Ali;Shokri, Ali
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.189-195
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    • 2014
  • Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

A NOTE ON OPERATORS ON FINSLER MODULES

  • TAGHAVI, A.;JAFARZADEH, JAFARZADEH
    • Honam Mathematical Journal
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    • v.28 no.4
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    • pp.533-541
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    • 2006
  • let E be a Finsler modules over $C^*$-algebras. A with norm-map $\rho$ and L(E) set of all A-linear bonded operators on E. We show that the canonical homomorphism ${\phi}:L(E){\rightarrow}L(E_I)$ sending each operator T to its restriction $T|E_I$ is injective if and only if I is an essential ideal in the underlying $C^*$-algebra A. We also show that $T{\in}L(E)$ is a bounded below if and only if ${\mid}{\mid}x{\mid}{\mid}={\mid}{\mid}{\rho}{\prime}(x){\mid}{\mid}$ is complete, where ${\rho}{\prime}(x)={\rho}(Tx)$ for all $x{\in}E$. Also, we give a necessary and sufficient condition for the equivalence of the norms generated by the norm map.

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