scholarly journals Set inner amenability for semigroups

2020 ◽  
Vol 4 (3) ◽  
pp. 176-183
Author(s):  
Moslem AMİNİ NİA ◽  
Ali EBADİAN
Keyword(s):  
Inner Amenability

scholarly journals Module character inner amenability of Banach algebras

2017 ◽  
Vol 11 (3) ◽  
pp. 173-179
Author(s):  
H. Sadeghi ◽  
M. Lashkarizadeh Bami
Keyword(s):  
Banach Algebras ◽  
Inner Amenability

scholarly journals Inner amenability, property Gamma, McDuff factors and stable equivalence relations

2017 ◽  
Vol 38 (7) ◽  
pp. 2618-2624 ◽  
Author(s):  
TOBE DEPREZ ◽  
STEFAAN VAES
Keyword(s):  
Probability Measure ◽  
Von Neumann Algebra ◽  
Amenable Group ◽  
Countable Group ◽  
Acta Math ◽  
Equivalence Relations ◽  
Orbit Equivalence ◽  
Von Neumann ◽  
Stable Equivalence ◽  
Inner Amenability

We say that a countable group $G$ is McDuff if it admits a free ergodic probability measure preserving action such that the crossed product is a McDuff $\text{II}_{1}$ factor. Similarly, $G$ is said to be stable if it admits such an action with the orbit equivalence relation being stable. The McDuff property, stability, inner amenability and property Gamma are subtly related and several implications and non-implications were obtained in Effros [Property $\unicode[STIX]{x1D6E4}$ and inner amenability. Proc. Amer. Math. Soc.47 (1975), 483–486], Jones and Schmidt [Asymptotically invariant sequences and approximate finiteness. Amer. J. Math.109 (1987), 91–114], Vaes [An inner amenable group whose von Neumann algebra does not have property Gamma. Acta Math.208 (2012), 389–394], Kida [Inner amenable groups having no stable action. Geom. Dedicata173 (2014), 185–192] and Kida [Stability in orbit equivalence for Baumslag–Solitar groups and Vaes groups. Groups Geom. Dyn.9 (2015), 203–235]. We complete the picture with the remaining implications and counterexamples.

On an open problem by Nasr-Isfahani on strict inner amenability

2013 ◽  
Vol 50 (1) ◽  
pp. 26-30
Author(s):  
Mohammad Ghanei ◽  
Mehdi Nemati
Keyword(s):  
Large Class ◽  
Open Problem ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Inner Amenability

For two locally compact groups G and H, we show that if L1(G) is strictly inner amenable, then L1(G × H) is strictly inner amenable. We then apply this result to show that there is a large class of locally compact groups G such that L1(G) is strictly inner amenable, but G is not even inner amenable.

Topological inner invariant means

2003 ◽  
Vol 40 (3) ◽  
pp. 293-299
Author(s):  
R. Memarbashi ◽  
A. Riazi
Keyword(s):  
Compact Group ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Invariant Means ◽  
Inner Amenability

For a locally compact group G, we investigate topological inner invariant means on L8(G) and its subspaces. In particular, we characterize strict inner amenability of L1(G) to study the relation between this notion and strict inner amenability of G.

Property Γ and Inner Amenability

1975 ◽  
Vol 47 (2) ◽  
pp. 483 ◽  
Author(s):  
Edward G. Effros
Keyword(s):  
Inner Amenability

Ergodic properties and harmonic functionals on locally compact quantum groups

2014 ◽  
Vol 25 (05) ◽  
pp. 1450051 ◽  
Author(s):  
Mehdi Nemati
Keyword(s):  
Quantum Groups ◽  
Compact Quantum Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Ergodic Properties ◽  
Locally Compact Quantum Groups ◽  
Locally Compact Quantum Group ◽  
Compact Quantum Groups ◽  
Inner Amenability

For a locally compact quantum group 𝔾, we generalize some notions of amenability such as amenability of locally compact quantum groups and inner amenability of locally compact groups to the case of right Banach L1(𝔾)-modules. Also, we investigate the concept of harmonic functionals over right Banach L1(𝔾)-modules and use these devices to study, among others, amenability of 𝔾.

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