scholarly journals P-Tensor Product for Group C*-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 627
Author(s):  
Yufang Li ◽  
Zhe Dong
Keyword(s):  
Tensor Product ◽  
Free Group ◽  
Discrete Group ◽  
Tensor Products ◽  
Haagerup Property ◽  
C Algebras ◽  
P Tensor

In this paper, we introduce new tensor products ⊗ p ( 1 ≤ p ≤ + ∞ ) on C ℓ p * ( Γ ) ⊗ C ℓ p * ( Γ ) and ⊗ c 0 on C c 0 * ( Γ ) ⊗ C c 0 * ( Γ ) for any discrete group Γ . We obtain that for 1 ≤ p < + ∞ C ℓ p * ( Γ ) ⊗ m a x C ℓ p * ( Γ ) = C ℓ p * ( Γ ) ⊗ p C ℓ p * ( Γ ) if and only if Γ is amenable; C c 0 * ( Γ ) ⊗ m a x C c 0 * ( Γ ) = C c 0 * ( Γ ) ⊗ c 0 C c 0 * ( Γ ) if and only if Γ has Haagerup property. In particular, for the free group with two generators F 2 we show that C ℓ p * ( F 2 ) ⊗ p C ℓ p * ( F 2 ) ≇ C ℓ q * ( F 2 ) ⊗ q C ℓ q * ( F 2 ) for 2 ≤ q < p ≤ + ∞ .

Finite Lattices of Projections in Factors and Approximately Finite C*-Algebras

1992 ◽  
Vol 35 (1) ◽  
pp. 116-125
Author(s):  
S. C. Power
Keyword(s):  
Tensor Product ◽  
General Result ◽  
Finite Lattice ◽  
Tensor Products ◽  
C Algebras ◽  
Finite Lattices

AbstractA unique factorisation theorem is obtained for tensor products of finite lattices of commuting projections in a factor. This leads to unique tensor product factorisations for reflexive subalgebras of the hyperfinite II1 factor which have irreducible finite commutative invariant projection lattices. It is shown that the finite refinement property fails for simple approximately finite C*-algebras, and this implies that there is no analogous general result for finite lattice subalgebras in this context.

scholarly journals The similarity problem for tensor products of certain C*-algebras

2004 ◽  
Vol 70 (3) ◽  
pp. 385-389 ◽  
Author(s):  
Florin Pop
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
C Algebras ◽  
Similarity Problem ◽  
Bounded Representation

We prove that every bounded representation of the tensor product of two C*-algebras, one of which is nuclear and contains matrices of any order, is similar to a *-representation.

scholarly journals QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450019 ◽  
Author(s):  
RALF MEYER ◽  
SUTANU ROY ◽  
STANISŁAW LECH WORONOWICZ
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Quantum Group ◽  
Quantum Groups ◽  
Tensor Products ◽  
Group Representations ◽  
Basic Properties ◽  
C Algebras ◽  
Twisted Tensor Product

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways, based on certain pairs of quantum group representations and based on covariant Hilbert space representations, respectively. We establish basic properties of the twisted tensor product and study some examples.

A CONTINUUM OF C*-NORMS ON (H) ⊗ (H) AND RELATED TENSOR PRODUCTS

2015 ◽  
Vol 58 (2) ◽  
pp. 433-443 ◽  
Author(s):  
NARUTAKA OZAWA ◽  
GILLES PISIER
Keyword(s):  
Tensor Product ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann ◽  
C Algebras ◽  
Injective Tensor Product ◽  
Algebraic Tensor Product

AbstractFor any pair M, N of von Neumann algebras such that the algebraic tensor product M ⊗ N admits more than one C*-norm, the cardinal of the set of C*-norms is at least 2ℵ0. Moreover, there is a family with cardinality 2ℵ0 of injective tensor product functors for C*-algebras in Kirchberg's sense. Let ${\mathbb B}$=∏nMn. We also show that, for any non-nuclear von Neumann algebra M⊂ ${\mathbb B}$(ℓ2), the set of C*-norms on ${\mathbb B}$ ⊗ M has cardinality equal to 22ℵ0.

scholarly journals Geometry of the tensor product of C*-algebras

1988 ◽  
Vol 104 (1) ◽  
pp. 119-127 ◽  
Author(s):  
D. P. Blecher
Keyword(s):  
Tensor Product ◽  
Crucial Role ◽  
Tensor Products ◽  
Operator Spaces ◽  
C Algebra ◽  
Geometrical Properties ◽  
C Algebras ◽  
Algebraic Tensor Product ◽  
Natural Way

When and ℬ are C*-algebras their algebraic tensor product ⊗ ℬ is a *-algebra in a natural way. Until recently, work on tensor products of C*-algebras has concentrated on norms α which make the completion ⊗α ℬ into a C*-algebra. The crucial role played by the Haagerup norm in the theory of operator spaces and completely bounded maps has produced some interest in more general norms (see [8; 12]). In this paper we investigate geometrical properties of algebra norms on ⊗ ℬ. By an ‘algebra norm’ we mean a norm which is sub-multiplicative: α(u.v) ≤ ≤ α(u).α(v).

scholarly journals TENSOR PRODUCTS OF MAXIMAL ABELIAN SUBALGBERAS OF C*-ALGEBRAS

2008 ◽  
Vol 50 (2) ◽  
pp. 209-216 ◽  
Author(s):  
SIMON WASSERMANN
Keyword(s):  
Tensor Product ◽  
Tensor Products ◽  
Extension Property ◽  
Approximate Identity ◽  
Extension Problem ◽  
C Algebras ◽  
Algebraic Tensor Product ◽  
Standing Question

AbstractIt is shown that if C1 and C2 are maximal abelian self-adjoint subalgebras (masas) of C*-algebras A1 and A2, respectively, then the completion C1 ⊗ C2 of the algebraic tensor product C1 ⊙ C2 of C1 and C2 in any C*-tensor product A1 ⊗βA2 is maximal abelian provided that C1 has the extension property of Kadison and Singer and C2 contains an approximate identity for A2. Examples are given to show that this result can fail if the conditions on the two masas do not both hold. This gives an answer to a long-standing question, but leaves open some other interesting problems, one of which turns out to have a potentially intriguing implication for the Kadison-Singer extension problem.

scholarly journals Boundary Action On Simple Reduced Group C*-Algebras

2021 ◽  
Vol 03 (01) ◽  
pp. 1-15
Author(s):  
V.A. Onuche ◽  
◽  
T.J Alabiand ◽  
O.F. Ajayi ◽  
◽  
...  
Keyword(s):  
Simple Group ◽  
Free Group ◽  
Discrete Group ◽  
Crossed Products ◽  
Ideal Structure ◽  
Stability Properties ◽  
C Algebras ◽  
Reduced Group ◽  
The Stability

A connection between boundary actions, ideal structure of reduced crossed products and C*-simple group is imminent.We investigate the stability properties for discrete group pioneered by powers and show that the non-abelian free group on two generators is C*-simple.Kalantar and Kennedy [32, Theorem 6.2] is now extended. Some examples are given using characterization of C*-simplicity obtained by Kalantar, Kennedy, Breuillard, and Ozawa [10, Theorem 3.1]

scholarly journals NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS

2015 ◽  
Vol 58 (1) ◽  
pp. 119-136
Author(s):  
KATSUNORI KAWAMURA
Keyword(s):  
Tensor Product ◽  
Free Group ◽  
Free Groups ◽  
Full Group ◽  
C Algebras ◽  
Direct Sum ◽  
Product Formulas

AbstractLeti ${\Bbb F}$n be the free group of rank n and let $\bigoplus C^{*}({\Bbb F}_{n})$ denote the direct sum of full group C*-algebras $C^{*}({\Bbb F}_{n})$ of ${\Bbb F}_{n} (1\leq n<\infty$). We introduce a new comultiplication Δϕ on $\bigoplus C^{*}({\Bbb F}_{n})$ such that $(\bigoplus C^{*}({\Bbb F}_{n}),\,\Delta_{\varphi})$ is a non-cocommutative C*-bialgebra. With respect to Δϕ, the tensor product π⊗ϕπ′ of any two representations π and π′ of free groups is defined. The operation ×ϕ is associative and non-commutative. We compute its tensor product formulas of several representations.

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