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A wide new class of subsets of a Banach space X named coarse p-limited sets ( 1 ≤ p < ∞ ) is introduced by considering weak* p-summable sequences in X ′ instead of weak* null sequences. We study its basic properties and compare it with the class of compact and weakly compact sets. Results concerning the relationship of coarse p-limited sets with operators are obtained. [ABSTRACT FROM AUTHOR]

We study extreme values of group-indexed stable random fields for discrete groups G acting geometrically on spaces X in the following cases: (1) G acts properly discontinuously by isometries on a CAT(-1) space X, (2) G is a lattice in a higher rank Lie group, acting on a symmetric space X, and (3) G is the mapping class group of a surface acting on its Teichmüller space. The connection between extreme values and the geometric action is mediated by the action of the group G on its limit set equipped with the Patterson–Sullivan measure. Based on motivation from extreme value theory, we introduce an invariant of the action called extremal cocycle growth which measures the distortion of measures on the boundary in comparison to the movement of points in the space X and show that its non-vanishing is equivalent to finiteness of the Bowen–Margulis measure for the associated unit tangent bundle U(X/G) provided X/G has non-arithmetic length spectrum. As a consequence, we establish a dichotomy for the growth-rate of a partial maxima sequence of stationary symmetric α -stable ( 0 < α < 2 ) random fields indexed by groups acting on such spaces. We also establish analogous results for normal subgroups of free groups. [ABSTRACT FROM AUTHOR]

Let X be a complex Banach space with dim X ≥ 2 , and A ⊆ B (X) be a standard operator algebra. We show that a linear mapping δ : A → A is anti-derivable at zero (i.e., x y = 0 in A implies y δ (x) + δ (y) x = 0 ) if and only if δ = 0 . [ABSTRACT FROM AUTHOR]

For a continuous self-map f on a compact metric space X, we provide two simple examples: the first confirms that shadowing of (X, f) is not inherited by (M (X) , f ^) in general, and the other satisfies that both (X, f) and (M (X) , f ^) have no Li–Yorke pair, where M (X) be the space of all Borel probability measures on X. Then we prove that chain transitivity of (X, f) implies chain mixing of (M (X) , f ^) , and provide an example to deny the converse. For a non-autonomous system (X , f 0 , ∞) , we prove that weak mixing of (M (X) , f ^ 0 , ∞) implies that of (X , f 0 , ∞) , and give an example to deny the converse, where f 0 , ∞ = { f n } n = 0 ∞ is a sequence of continuous self-maps on X. We also prove that if f n is surjective for all n ≥ 0 , then chain mixing of (M (X) , f ^ 0 , ∞) always holds true, and shadowing of (M (X) , f ^ 0 , ∞) implies mixing of (X , f 0 , ∞) . If X = I is an interval, we obtain a sharp condition such that transitivity is equivalent between (I, f) and (M (I) , f ^) . Although (M (I) , f ^) has infinite topological entropy for any transitive system (I, f), we give an example such that (I , f 0 , ∞) is transitive but (M (I) , f ^ 0 , ∞) has zero topological entropy. [ABSTRACT FROM AUTHOR]

For a homeomorphism T : X → X of a compact metric space X, the stabilized automorphism group Aut (∞) (T) consists of all self-homeomorphisms of X which commute with some power of T. Motivated by the study of these groups in the context of shifts of finite type, we introduce a certain entropy for groups called local P entropy. We show that when (X, T) is a non-trivial mixing shift of finite type, the local P entropy of the group Aut (∞) (T) is determined by the topological entropy of (X, T). We use this to give a complete classification of the isomorphism type of the stabilized automorphism groups of full shifts. [ABSTRACT FROM AUTHOR]

For a pair potential Φ in a general underlying space X satisfying some natural and sufficiently general conditions in the sense of Penrose (J Math Phys 4:1312, 1963) and Poghosyan and Ueltschi (J Math Phys 50:053509, 2009) together with a locally finite measure ϱ on X we define by means of the so-called Ursell kernel a function r which is shown to be the correlation function of a unique process G , the limiting Gibbs process for (Φ , ϱ) with empty boundary conditions. This process is exhibited as a Gibbs process in the sense of Dobrushin, Lanford and Ruelle for a class of pair potentials, which contains classical stable and hard-core potentials that are called Penrose potentials here. Particularly, a class of positive potentials is included. Finally, for some class of Penrose potentials, we show that G is the unique Gibbs process for Φ . We use the classical method of Kirkwood–Salsburg equations. A decisive role is played by a generalization of Ruelle's estimate for correlation functions. [ABSTRACT FROM AUTHOR]

A subspace H of a rearrangement invariant space X is strongly embedded in X if, on H, convergence in the X-norm is equivalent to convergence in measure. Necessary and sufficient conditions on an Orlicz function M are obtained under which the unit ball of any subspace strongly embedded in the Orlicz space LM has equi-absolutely continuous norms in LM. [ABSTRACT FROM AUTHOR]

In a Hilbert space X, we consider the abstract problem M ∗ d dt My t = Ly t + f t z , 0 ≤ t ≤ τ , My 0 = My 0 where L is a closed linear operator in X and M ∈ ℒ(X) is not necessarily invertible, z ∈ X. Given the additional information Φ[My(t)] = g(t) with Φ ∈ X*, g ∈ C1([0, τ];ℂ), we are concerned with the determination of the conditions under which we can identify f ∈ C([0, τ];ℂ) such that y be a strict solution to the abstract problem, i.e., My ∈ C1([0, τ];X), Ly ∈ C([0, τ];X). A similar problem is considered for general second-order equations in time. Various examples of these general problems are given. [ABSTRACT FROM AUTHOR]

We investigate the mortar finite element method for second order elliptic boundary value problems on domains which are decomposed into patches Ω k with tensor-product NURBS parameterizations. We follow the methodology of IsoGeometric Analysis (IGA) and choose discrete spaces X h , k on each patch Ω k as tensor-product NURBS spaces of the same or higher degree as given by the parameterization. Our work is an extension of Brivadis et al. (Comput Methods Appl Mech Eng 284:292–319, 2015) and highlights several aspects which did not receive full attention before. In particular, by choosing appropriate spaces of polynomial splines as Lagrange multipliers, we obtain a uniform infsup-inequality. Moreover, we provide a new additional condition on the discrete spaces X h , k which is required for obtaining optimal convergence rates of the mortar method. Our numerical examples demonstrate that the optimal rate is lost if this condition is neglected. [ABSTRACT FROM AUTHOR]

For a group G and ω ∈ Z 3 (G , U (1)) , an ω -anomalous action on a C*-algebra B is a U (1) -linear monoidal functor between 2-groups , where the latter denotes the 2-group of ∗ -automorphisms of B. The class [ ω ] ∈ H 3 (G , U (1)) is called the anomaly of the action. We show that for every n ≥ 2 and every finite group G, every anomaly can be realized on the stabilization of a commutative C*-algebra C (M) ⊗ K for some closed connected n-manifold M. We also show that although there are no anomalous symmetries of Roe C*-algebras of coarse spaces, for every finite group G, every anomaly can be realized on the Roe corona C ∗ (X) / K of some bounded geometry metric space X with property A. [ABSTRACT FROM AUTHOR]

Given a reflexive Banach space X, we consider a class of functionals Φ ∈ C 1 (X , R) that do not behave in a uniform way, in the sense that the map t ↦ Φ (t u) , t > 0 , does not have a uniform geometry with respect to u ∈ X . Assuming instead such a uniform behavior within an open cone Y ⊂ X \ { 0 } , we show that Φ has a ground state relative to Y. Some further conditions ensure that this relative ground state is the (absolute) ground state of Φ . Several applications to elliptic equations and systems are given. [ABSTRACT FROM AUTHOR]

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J(n) of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator J(n) and its descendants. For perturbations on null planes only moments of J(n) itself contribute. [ABSTRACT FROM AUTHOR]

Let ? be a unimodular complex number, and let k be an integer. Then ?Ak is an isometry for any isometry A of a complex Banach space. It is shown that if f is an analytic function on the unit circle sending an isometry to an isometry for any norm, then f has the form z ? ?zk for some unimodular ? and integer k. The same conclusion on f can be deduced if f is merely continuous and preserves the isometries of some special classes of norms on a fixed finite-dimensional complex Banach space. The result is extended to real Banach spaces X with dimX = 4, and it is shown that one cannot get the same conclusion on f if dimX <4. Further extensions of these results are also considered. [ABSTRACT FROM AUTHOR]