• Corpus ID: 115175413

THE ARENS REGULARITY AND WEAK TOPOLOGICAL CENTER OF MODULE ACTIONS

@article{Azar2010THEAR,
  title={THE ARENS REGULARITY AND WEAK TOPOLOGICAL CENTER OF MODULE ACTIONS},
  author={Kazem Haghnejad Azar},
  journal={arXiv: Functional Analysis},
  year={2010}
}
  • K. Azar
  • Published 17 March 2010
  • Mathematics
  • arXiv: Functional Analysis
Let A be a Banach algebra and A �� be the second dual of it. We define ˜ Z1(A �� ) as a weak topological center of A �� with respect to first Arens product and find some relations between it and the topological center of A �� . We also extend this new definition into the module actions and find relationship between weak topological center of module actions and reflexivity or Arens regu- larity of some Banach algebras, and we investigate some applications of this new definition in the weak… 
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References

SHOWING 1-10 OF 26 REFERENCES
Topological centers of certain dual algebras
Let A be a Banach algebra with a bounded approximate identity. Let Z1 and Z2 be, respectively, the topological centers of the algebras A** and (A*A)*. In this paper, for weakly sequentially complete…
Weak amenability of module extensions of banach algebras
We start by discussing general necessary and sufficient conditions for a module extension Banach algebra to be n-weakly amenable, for n = 0,1,2;... Then we investigate various special cases. All…
Arens regularity of module actions
We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if A has a brai (blai), then the right (left) module action of A on Ais Arens…
A SIMPLE CONDITION ENSURING THE ARENS REGULARITY OF BILINEAR MAPPINGS
We give a simple criterion for certain Banach algebras to be Arens regular, which applies in particular to the algebras /' with pointwise multiplication, ^"(G), where G is a compact group with…
Arens regularity of weakly sequentially complete Banach algebras
In this paper we prove the following result: Let A be a nonunital Banach algebra with a bounded approximate identity. Then A cannot be both Arens regular and weakly sequentially complete. The paper…
Arens Regularity of the Algebra A ^ ⊗ B
Let A and B be two Banach algebras. On the protective tensor product A ® B of A and B there exists a natural algebra structure. In this note we study Arens regularity of the Banach algebra A ® B.
On a conjecture by Ghahramani–Lau and related problems concerning topological centres
The Second Transpose of a Derivation
Let A be a Banach algebra, and let D: A → A* be a continuous derivation, where A* is the topological dual space of A. The paper discusses the situation when the second transpose D**: A** → (A**)* is…
Some stability properties of Arens regular bilinear operators
In this paper we present three results about Arens regular bilinear operators. These are: (a). Let X , Y be two Banach spaces, K a compact Hausdorff space, µ a Borel measure on K and m: X × Y →ℂ a…
The adjoint of a bilinear operation
is an extension of m. Recall that X, Y, Z are naturally embeddable in X-, Y--, Z-resp. Moreover, certain properties, such as associativity, when m has them, are transmitted to m*** (this makes sense…
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