AMENABILITY AND MODULES FOR ARENS PRODUCT ALGEBRAS

2014 ◽  
Vol 66 (1) ◽  
pp. 295-321 ◽  
Author(s):  
R. Stokke
Keyword(s):  
Arens Product

scholarly journals The second dual of C0 (S, A)

1994 ◽  
Vol 56 (3) ◽  
pp. 303-313
Author(s):  
Stephen T. L. Choy ◽  
James C. S. Wong
Keyword(s):  
Function Space ◽  
Simple Proof ◽  
Representation Theorem ◽  
Generalized Functions ◽  
Arens Product ◽  
Nikodym Property ◽  
Second Dual ◽  
Vector Valued Function ◽  
Vector Valued

AbstractThe second dual of the vector-valued function space C0(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodým property. As an application we present a simple proof that C0 (S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure μh is given, where , h ∈ L∞ (|μ;|, A**) and μh is defined by the Arens product.

THE SECOND TRANSPOSE OF A DERIVATION

2001 ◽  
Vol 64 (3) ◽  
pp. 707-721 ◽  
Author(s):  
H. G. DALES, ◽  
A. RODRÍGUEZ-PALACIOS ◽  
M. V. VELASCO
Keyword(s):  
Banach Algebra ◽  
Dual Space ◽  
Arens Product

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 also a derivation in the case where A** has the first Arens product.

scholarly journals Amenability and topological centres of the second duals of Banach algebras

2002 ◽  
Vol 65 (2) ◽  
pp. 191-197 ◽  
Author(s):  
F. Ghahramani ◽  
J. Laali
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Dual Algebra ◽  
Arens Product ◽  
Weak Amenability ◽  
Arens Regularity ◽  
Second Dual

Let  be a Banach algebra and let ** be the second dual algebra of  endowed with the first or the second Arens product. We investigate relations between amenability of ** and Arens regularity of  and the rôle topological centres in amenability of **. We also find conditions under which weak amenability of ** implies weak amenability of .

Double multipliers andA*-algebras of the first kind

1987 ◽  
Vol 102 (3) ◽  
pp. 507-516 ◽  
Author(s):  
M. S. Kassem ◽  
K. Rowlands
Keyword(s):  
Multiplier Algebra ◽  
Arens Product ◽  
Norm Closure ◽  
Multiplier Algebras

LetAbe anA*-algebra and letdenote its auxiliary norm closure. The multiplier algebras of dualA*-algebras of the first kind have been studed by Tomiuk [12], [13] and Wong[15]. In this paper we study the double multiplier algebra ofA*-algebras of the first kind. In particular, we prove that, ifAis anA*-algebra of the first kind, then the double multiplier algebraM(A) ofAis *-isomorphic and (auxiliary norm) isometric to a subalgebra ofM(), extending in the process some results established by Tomiuk[12]. We also consider the embedding of the double multiplier algebra ofAin**, when the latter is regarded as an algebra with the Arens product, and, in particular, we show that, for an annihilator A*-algebra,M(A) is *-isomorphic and (auxiliary norm) isometric to**.

The Second Conjugates of Certain Banach Algebras

1975 ◽  
Vol 27 (5) ◽  
pp. 1029-1035 ◽  
Author(s):  
Pak-Ken Wong
Keyword(s):  
Recent Result ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Arens Product ◽  
Conjugate Space ◽  
Natural Extensions ◽  
Semisimple Banach Algebra

Let A be a Banach algebra and A** its second conjugate space. Arens has denned two natural extensions of the product on A to A**. Under either Arens product, A** becomes a Banach algebra. Let A be a semisimple Banach algebra which is a dense two-sided ideal of a B*-algebra B and R** the radical of (A**, o). We show that A** = Q ⊕ R**, where Q is a closed two-sided ideal of A**, o). This was inspired by Alexander's recent result for simple dual A*-algebras (see [1, p. 573, Theorem 5]). We also obtain that if A is commutative, then A is Arens regular.

Unit Elements in the Double Dual of a Subalgebra of the Fourier Algebra A(G)

2009 ◽  
Vol 61 (2) ◽  
pp. 382-394
Author(s):  
Tianxuan Miao
Keyword(s):  
Compact Group ◽  
Banach Algebra ◽  
Locally Compact Group ◽  
Approximate Identity ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Arens Product ◽  
The Right ◽  
Topological Centers ◽  
The Relationship

Abstract. Let 𝒜 be a Banach algebra with a bounded right approximate identity and let ℬ be a closed ideal of 𝒜. We study the relationship between the right identities of the double duals ℬ** and 𝒜** under the Arens product. We show that every right identity of ℬ** can be extended to a right identity of 𝒜** in some sense. As a consequence, we answer a question of Lau and Ülger, showing that for the Fourier algebra A(G) of a locally compact group G, an element ϕ ∈ A(G)** is in A(G) if and only if A(G)ϕ ⊆ A(G) and Eϕ = ϕ for all right identities E of A(G)**. We also prove some results about the topological centers of ℬ** and 𝒜**.

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