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Old and new results on Allan's GB*-algebras

Maria Fragoulopoulou, Atsushi Inoue, Klaus-Detlef Kürsten (2010)

Banach Center Publications

This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication...

On character amenable Banach algebras

Z. Hu, M. Sangani Monfared, T. Traynor (2009)

Studia Mathematica

We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A...

On Gelfand-Mazur theorem on a class of F -algebras

E. Anjidani (2014)

Topological Algebra and its Applications

A topological algebra A is said to be fundamental if there exists b > 1 such that for every sequence (xn) in A, (xn) is Cauchy whenever the sequence bn(xn − xn-1) tends to zero as n → ∞. Let A be a complex unital fundamental F-algebra with bounded elements such that A* separates the points on A. Then we prove that the spectrum σ(a) of every element a ∈ A is nonempty compact. Moreover, if A is a division algebra, then A is isomorphic to the complex numbers ℂ. This result is a generalization of...

On Local Uniform Topological Algebras

Oukhouya, Ali (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.Every unital "combinatorially regular" commutative uniform complete locally m-convex algebra is local.

On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

On topological algebras

G. A. Stavrakas (1991)

Πανελλήνιο Συνέδριο Μαθηματικής Παιδείας

Operator Connes-amenability of completely bounded multiplier Banach algebras

Bahman Hayati, Abasalt Bodaghi, Massoud Amini (2019)

Archivum Mathematicum

For a completely contractive Banach algebra B , we find conditions under which the completely bounded multiplier algebra ℳ c b ( B ) is a dual Banach algebra and the operator amenability of B is equivalent to the operator Connes-amenability of ℳ c b ( B ) . We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.

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