On the sup-norm closure of theL ∞-representation algebraR(S) of a foundation semigroupS

1996 ◽  
Vol 52 (1) ◽  
pp. 389-392
Author(s):  
M. Lashkarizadeh Bami
Keyword(s):  
Norm Closure

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**.

scholarly journals The compactum of a semi-simple commutative Banach algebra

1984 ◽  
Vol 7 (4) ◽  
pp. 821-822
Author(s):  
Abduliah H. Al-Moajil
Keyword(s):  
Banach Algebra ◽  
Commutative Banach Algebra ◽  
Norm Closure ◽  
Finite Sums

LetAbe a commutative semi-simple Banach algebra such that the set consisting of finite sums of elements from minimal left ideals coincides with that of finite sums of elements from minimal right ideals. LetS(A)(the socle ofA) denote this set. LetC(A)denote the set of elementsxinAsuch that the mapa→xaxis compact. It is shown thatC(A)is the norm closure ofS(A).

scholarly journals On Hilbert dynamical systems

2011 ◽  
Vol 32 (2) ◽  
pp. 629-642 ◽  
Author(s):  
ELI GLASNER ◽  
BENJAMIN WEISS
Keyword(s):  
Dynamical Systems ◽  
Periodic Function ◽  
Harmonic Analysis ◽  
Dual Group ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Norm Closure ◽  
Weakly Almost Periodic ◽  
Stieltjes Transforms

AbstractReturning to a classical question in harmonic analysis, we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers ℤ which is not in the norm-closure of the algebra B(ℤ) of Fourier–Stieltjes transforms of measures on the dual group $\hat {\mathbb {Z}}=\mathbb {T}$, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.

scholarly journals Norm-closure of the barrier cone in normed linear spaces

2004 ◽  
Vol 132 (10) ◽  
pp. 2911-2915 ◽  
Author(s):  
Samir Adly ◽  
Emil Ernst ◽  
Michel Théra
Keyword(s):  
Linear Spaces ◽  
Norm Closure ◽  
Normed Linear Spaces ◽  
Barrier Cone

Predual of the Multiplier Algebra of Ap(G) and Amenability

2004 ◽  
Vol 56 (2) ◽  
pp. 344-355 ◽  
Author(s):  
Tianxuan Miao
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Linear Span ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Norm Closure ◽  
Multiplier Space ◽  
Dual Banach Space

AbstractFor a locally compact group G and 1 < p < ∞, let Ap(G) be the Herz-Figà-Talamanca algebra and let PMp(G) be its dual Banach space. For a Banach Ap(G)-module X of PMp(G), we prove that the multiplier space ℳ(Ap(G); X*) is the dual Banach space of QX, where QX is the norm closure of the linear span Ap(G)X of u f for u 2 Ap(G) and f ∈ X in the dual of ℳ(Ap(G); X*). If p = 2 and PFp(G) ⊆ X, then Ap(G)X is closed in X if and only if G is amenable. In particular, we prove that the multiplier algebra MAp(G) of Ap(G) is the dual of Q, where Q is the completion of L1(G) in the ‖ · ‖M-norm. Q is characterized by the following: f ∈ Q if an only if there are ui ∈ Ap(G) and fi ∈ PFp(G) (i = 1; 2, … ) with such that on MAp(G). It is also proved that if Ap(G) is dense in MAp(G) in the associated w*-topology, then the multiplier norm and ‖ · ‖Ap(G)-norm are equivalent on Ap(G) if and only if G is amenable.

C*-Convexity and the Numerical Range

2000 ◽  
Vol 43 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Bojan Magajna
Keyword(s):  
Convex Hull ◽  
Extreme Point ◽  
Von Neumann Algebra ◽  
Numerical Range ◽  
Von Neumann ◽  
Norm Closure

AbstractIf A is a prime C*-algebra, a ∈ A and λ is in the numerical range W(a) of a, then for each ε > 0 there exists an element h ∈ A such that . If λ is an extreme point of W(a), the same conclusion holds without the assumption that A is prime. Given any element a in a von Neumann algebra (or in a general C*-algebra) A, all normal elements in the weak* closure (the norm closure, respectively) of the C*-convex hull of a are characterized.

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