Complete Normed Algebras

Bonsall, F. F.; Duncan, John F. R.

doi:10.1007/978-3-642-65669-9

Cited by 1,110 publications

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“…This implies that R S is surjective. The rest in (1) is clear, as is (2), and the isometric nature of the induced map R ′ S in (3) follows again from the above extension property of elements of C(S).…”

Section: Preliminariesmentioning

confidence: 89%

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Jeu

Tomiyama

2016

Advances in Mathematics

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Abstract. If X is a compact Hausdorff space and σ is a homeomorphism of X, then a Banach algebra ℓ 1 (Σ) of crossed product type is naturally associated with this topological dynamical system Σ = (X, σ). If X consists of one point, then ℓ 1 (Σ) is the group algebra of the integers.We study the algebraically irreducible representations of ℓ 1 (Σ) on complex vector spaces, its primitive ideals, and its structure space. The finite dimensional algebraically irreducible representations are determined up to algebraic equivalence, and a sufficiently rich family of infinite dimensional algebraically irreducible representations is constructed to be able to conclude that ℓ 1 (Σ) is semisimple. All primitive ideals of ℓ 1 (Σ) are selfadjoint, and ℓ 1 (Σ) is Hermitian if there are only periodic points in X. If X is metrizable or all points are periodic, then all primitive ideals arise as in our construction. A part of the structure space of ℓ 1 (Σ) is conditionally shown to be homeomorphic to the product of a space of finite orbits and T. If X is a finite set, then the structure space is the topological disjoint union of a number of tori, one for each orbit in X. If all points of X have the same finite period, then it is the product of the orbit space X/Z and T. For rational rotations of T, this implies that the structure space is homeomorphic to T 2 .

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Section: Preliminariesmentioning

confidence: 89%

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Jeu

Tomiyama

2016

Advances in Mathematics

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“…Proof. Suppose that E is an identity in A** with respect to the first Arens product, and let F be any element of (A*A +AA*) 1 Proof. Since A is regular, then A** has an identity with respect to either the first or second Arens product.…”

Section: A * a = { F -A : F E A * A E A } And A A * = {A * F : A E mentioning

confidence: 99%

On the Arens semi-regularity of weighted group algebras

Argün

Rowlands

1994

Glasgow Math. J.

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“…Therefore C0(ß, P) has a unique C*-norm by Proposition 2.5. 6. Some cases where uniqueness of C*-norm and "-regularity are equivalent.…”

Section: Then C*(b) Is Identified With the Algebra Of All C-valued Comentioning

confidence: 99%

The properties -regularity and uniqueness of 𝐶-norm in a general *-algebra

Barnes¹

1983

Trans. Amer. Math. Soc.

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Complete Normed Algebras

Cited by 1,110 publications

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Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

On the Arens semi-regularity of weighted group algebras

The properties -regularity and uniqueness of 𝐶-norm in a general *-algebra

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Complete Normed Algebras

Cited by 1,110 publications

References 0 publications

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

Algebraically irreducible representations and structure space of the Banach algebra associated with a topological dynamical system

On the Arens semi-regularity of weighted group algebras

The properties *-regularity and uniqueness of 𝐶*-norm in a general *-algebra

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Product

Resources

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The properties -regularity and uniqueness of 𝐶-norm in a general *-algebra