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MODULE AMENABILITY FOR SEMIGROUP ALGEBRAS
, 2002
"... Abstract. We extend the concept of amenability of a Banach algebra A to the case that there is an extra Amodule structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = ℓ 1 (S) as a Banach module over A = ℓ 1 (E) is module amenable iff S is amenable. ..."
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Abstract. We extend the concept of amenability of a Banach algebra A to the case that there is an extra Amodule structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = ℓ 1 (S) as a Banach module over A = ℓ 1 (E) is module amenable iff S is amenable
Amenable actions and almost invariant sets
 Proc. Amer. Math. Soc
"... Abstract. In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on MX, where M is a measure space. In parti ..."
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Cited by 18 (2 self)
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. In particular, we show that the action of Γ on X is amenable iff the shift Γ ↪→MX has almost invariant sets. 1.
On the amenability and Kunze–Stein property for groups acting on a tree
, 1988
"... We characterize the amenable groups acting on a locally finite tree. In particular if the tree is homogeneous and the group G acts transitively on the vertices then we prove that G is amenable iff G fixes one point of the boundary of the tree. Moreover we prove that a group G which acts transitively ..."
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Cited by 6 (0 self)
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We characterize the amenable groups acting on a locally finite tree. In particular if the tree is homogeneous and the group G acts transitively on the vertices then we prove that G is amenable iff G fixes one point of the boundary of the tree. Moreover we prove that a group G which acts
GroupInvariant Percolation on Graphs
 GAFA GEOMETRIC AND FUNCTIONAL ANALYSIS
, 1999
"... Let G be a closed group of automorphisms of a graph X. We relate geometric properties of G and X, such as amenability and unimodularity, to properties of Ginvariant percolation processes on X, such as the number of infinite components, the expected degree, and the topology of the components. Our fu ..."
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Cited by 112 (37 self)
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on any nonamenable Cayley graph has no infinite clusters. More generally, the same is true for any nonamenable graph with a unimodular transitive automorphism group. We show that G is amenable iff for all α<1, there is a Ginvariant site percolation process ω on X with P[x ∈ ω]>αfor all vertices x
TENSOR PRODUCTS AND TRANSFERABILITY OF SEMILATTICES
, 2005
"... Abstract. In general, the tensor product, A ⊗ B, of the lattices A and B with zero is not a lattice (it is only a joinsemilattice with zero). If A ⊗ B is a capped tensor product, then A ⊗ B is a lattice (the converse is not known). In this paper, we investigate lattices A with zero enjoying the pro ..."
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Cited by 2 (1 self)
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very effective condition (T). We prove that a finite lattice A is amenable iff it is sharply transferable as a joinsemilattice. For a general lattice A with zero, we obtain the result: A is amenable iff A is locally finite and every finite sublattice of A is transferable as a join
Uniform spanning forests
 ANN. PROBAB
, 2001
"... We study uniform spanning forest measures on infinite graphs, which are weak limits of uniform spanning tree measures from finite subgraphs. These limits can be taken with free (FSF) or wired (WSF) boundary conditions. Pemantle (1991) proved that the free and wired spanning forests coincide in Z d ..."
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Cited by 89 (23 self)
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d and that they give a single tree iff d � 4. In the present work, we extend Pemantle’s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks, potential theory, invariant percolation, and amenability. The uniform spanning forest model is related
THE POSITIVE FIXED POINTS OF BANACH LATTICES
"... Abstract. Let Z be a Banach lattice endowed with positive cone C and an ordercontinuous norm j.j. Let G be a leftamenable semigroup of positive linear endomorphisms of Z. Then the positive fixed points Co of Z under G form a lattice cone, and their linear span Z0 is a Banach lattice under an order ..."
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the composite of T and U under the semigroup operation. An element p G m*iG) is called a mean for G iff inf biT) < pib) < sup biT) for all b G G T€G T€G and leftinvariant for G iff T'mp=p forallTGG, where T'm denotes the adjoint of Tm. Following M. Day [1, p. 108] we call the semigroup G leftamenable
Epistemic modals in context.
 In Preyer and Peter (Eds),
, 2005
"... Abstract A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced so ..."
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Cited by 39 (1 self)
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Abstract A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced
Right Type Departmental Bulletin Paper
"... In this note, we discuss weak amenability of groups which is a generalization of amenability in some sense. Deflnition 1. A discrete group $\Gamma $ is said to be weakly amenable if there exists a net $(\varphi_{i}) $ of finitely supported functions on $\Gamma $ such that $\varphi_{i}arrow 1 $ poin ..."
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In this note, we discuss weak amenability of groups which is a generalization of amenability in some sense. Deflnition 1. A discrete group $\Gamma $ is said to be weakly amenable if there exists a net $(\varphi_{i}) $ of finitely supported functions on $\Gamma $ such that $\varphi_{i}arrow 1
The computational contents of ramified corecurrence
"... Abstract. The vast power of iterated recurrence is tamed by data ramification: if a function over words is definable by ramified recurrence and composition, then it is feasible, i.e. computable in polynomial time, i.e. any computation using the first n input symbols can have at most p(n) distinct c ..."
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is by multicursor finite state transducer on streams. A consequence is that a function over finite streams is definable by ramified corecurrence iff it is Turingcomputable in logarithmic space. Such corecursive definitions over finite streams are of practical interest, because large finite data
Results 1  10
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