C*‐norms for tensor products of discrete group C*‐algebras

Wiersma, Matthew

doi:10.1112/blms/bdu115

Cited by 8 publications

(10 citation statements)

References 13 publications

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“…This paper has inspired further work by a number of other authors (see [2,12,13,28,29]). Though Brown and Guentner defined L p -representations in the context of discrete groups, their definitions and basic results generalize immediately to our context of locally compact groups.…”

Section: Preliminaries On Lmentioning

confidence: 70%

“…Identify copies of F 2 in Γ 1 ×Γ 2 and let ∆ denote the diagonal subgroup of F 2 ×F 2 ⊂ Γ 1 ×Γ 2 . In the proof of [29,Theorem 3.2] a Fourier-Stieltjes space B σ satisfying the above conditions is constructed with the property that B σ | ∆ contains the constant function 1. Then B ℓ p (Γ 1 ×Γ 2 ) does not contain B σ since otherwise B ℓ p (∆) would contain the constant 1 and, hence, B ℓ p (∆) would be all of B(∆).…”

Section: Proof Clearly We Have Thatmentioning

confidence: 99%

“…Evidencing their usefulness, the L p -Fourier-Stieltjes algebras were used in [29] to find many intermediate C * -norms on tensor products of group C * -algebras. The L p -Fourier and Fourier-Stieltjes algebras are ideals of the Fourier-Stieltjes algebra corresponding to coefficient functions of L p -representations.…”

Section: Introductionmentioning

confidence: 99%

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Lp-Fourier and Fourier–Stieltjes algebras for locally compact groups

Wiersma

2015

Journal of Functional Analysis

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Section: Preliminaries On Lmentioning

confidence: 70%

Section: Proof Clearly We Have Thatmentioning

confidence: 99%

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Lp-Fourier and Fourier–Stieltjes algebras for locally compact groups

Wiersma

2015

Journal of Functional Analysis

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“…This is the C*-algebra of operators on the Hilbert space 2 (F 2 )-with canonical basis ( h ) h∈F 2generated by the unitary operators u g ( h ) = gh for g ∈ F 2 . In fact the tensor product C * r (F 2 ) C * r (F 2 ) has the largest possible number of cross C*-norms: continuum many [88]. Another important example of C*-algebra that is not nuclear is B (H ) when H is the separable infinite-dimensional Hilbert space [87].…”

Section: Tensor Productsmentioning

confidence: 99%

The Classification Problem for Automorphisms of C*-Algebras

Lupini¹

2015

Bull. symb. log

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We present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory. §1. Introduction. Borel complexity theory is an area of logic that studies, generally speaking, the relative complexity of classification problems in mathematics. The main ideas and methods for such a study come from descriptive set theory, which can be described as the analysis of definable sets in Polish spaces and their properties. In the framework of Borel complexity theory, a classification problem is regarded as an equivalence relation on a Polish space. Perhaps after a suitable parametrization, this virtually covers almost all concrete classification problems in mathematics.Under the assumption that the classes of objects under consideration are naturally parameterized by the points of a Polish space, it is to be expected-and demanded-that a satisfactory classification satisfy some constructibility assumption. A sensible notion of constructibility is to be Borel measurable with respect to the given parameterizations. This leads to the following definition, first introduced and studied in [33]. Suppose that E, E are equivalence relations on standard Borel spaces X, X . A Borel reduction from E to E is a Borel function f : X → X such thatfor every x 1 , x 2 ∈ X . The function f can be seen as a constructive way to assign to the objects of X complete invariants up to E that are E -classes. Equivalently a Borel reduction can be seen as an embedding of the quotient space X/E into the quotient space X /E that is "definable", in the sense that it admits a Borel lifting from X to X .

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“…For example, the binormal C * -tensor product M ⊗ bin N of von Neumann algebras M and N is studied by Effros and Lance in [2]. More recently, Ozawa and Pisier constructed a continuum of C * -norms on B(H) ⊙ B(H) (see [4]), where H is the infinite dimensional separable Hilbert space, and the author constructed a continuum of C * -norms on algebraic tensor products of certain group C * -algebras (see [6]).…”

Section: Introductionmentioning

confidence: 99%

Weak* tensor products for von Neumann algebras

Wiersma¹

2016

J. Operator Theory

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The category of C * -algebras is blessed with many different tensor products. In contrast, virtually the only tensor product ever used in the category of von Neumann algebras is the normal spatial tensor product. We propose a definition of what a generic tensor product in this category should be. We call these weak* tensor products.For von Neumann algebras M and N , there are, in general, many choices of weak* tensor completions of the algebraic tensor product M ⊙ N . In fact, we demonstrate that M has the property that M ⊙ N has a unique weak* tensor product completion for every von Neumann algebra N if and only if M is completely atomic, i.e., is a direct product of type I factors. This in particular implies that even abelian von Neumann algebras need not have this property. As an application of the theory developed throughout the paper, we construct 2 c nonequivalent weak* tensor product completions of L ∞ (R) ⊙ L ∞ (R).

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C‐norms for tensor products of discrete group C‐algebras

Cited by 8 publications

References 13 publications

Lp-Fourier and Fourier–Stieltjes algebras for locally compact groups

Lp-Fourier and Fourier–Stieltjes algebras for locally compact groups

The Classification Problem for Automorphisms of C*-Algebras

Weak* tensor products for von Neumann algebras

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