On the Jordan model operators
Hari Bercovici (1977)
Studia Mathematica
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Hari Bercovici (1977)
Studia Mathematica
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M. Mateljević (1975)
Matematički Vesnik
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Peng Cao, Shanli Sun (2008)
Studia Mathematica
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It is proved that if is a Jordan operator on a Hilbert space with the Jordan decomposition , where is normal and is compact and quasinilpotent, i = 1,2, and the Lie algebra generated by J₁,J₂ is an Engel Lie algebra, then the Banach algebra generated by J₁,J₂ is an Engel algebra. Some results for normal operators and Jordan operators on Banach spaces are given.
Jinchuan Hou, Chi-Kwong Li, Ngai-Ching Wong (2008)
Studia Mathematica
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Let ₁, ₂ be (not necessarily unital or closed) standard operator algebras on locally convex spaces X₁, X₂, respectively. For k ≥ 2, consider different products on elements in , which covers the usual product and the Jordan triple product T₁ ∗ T₂ = T₂T₁T₂. Let Φ: ₁ → ₂ be a (not necessarily linear) map satisfying whenever any one of ’s has rank at most one. It is shown that if the range of Φ contains all rank one and rank two operators then Φ must be a Jordan isomorphism multiplied...
M. Laczkovich (2003)
Fundamenta Mathematicae
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Let denote the isometry group of . We prove that if G is a paradoxical subgroup of then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system of Jordan domains with differentiable boundaries and of the same volume such that has the cardinality of the continuum, and for every amenable subgroup G of , the elements of are not G-equidecomposable; moreover, their interiors are not G-equidecomposable...
Chi-Kwong Li, Nung-Sing Sze (2006)
Studia Mathematica
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Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of by . This includes the usual product and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying such that ϕ: V → V has...
Mikio Kato, Lech Maligranda, Yasuji Takahashi (2001)
Studia Mathematica
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Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the -constant, which implies that a Banach space with -constant less than 5/4 has the fixed point property. ...
Paul Larson, Paul McKenney (2016)
Fundamenta Mathematicae
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We study conditions on automorphisms of Boolean algebras of the form (where λ is an uncountable cardinal and is the ideal of sets of cardinality less than κ ) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every automorphism of which is trivial on all sets of cardinality κ⁺ is trivial, and that implies both that every automorphism of (ℝ)/Fin is trivial on a cocountable set and that every automorphism of (ℝ)/Ctble is trivial. ...
F. Ghahramani, J. McClure (1992)
Studia Mathematica
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We find representations for the automorphisms, derivations and multipliers of the Fréchet algebra of locally integrable functions on the half-line . We show, among other things, that every automorphism θ of is of the form , where D is a derivation, X is the operator of multiplication by coordinate, λ is a complex number, a > 0, and is the dilation operator (, ). It is also shown that the automorphism group is a topological group with the topology of uniform convergence...
Arya Chandran, Neha Elizabeth Thomas, K. Vishnu Namboothiri (2022)
Czechoslovak Mathematical Journal
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Menon’s identity is a classical identity involving gcd sums and the Euler totient function . A natural generalization of is the Klee’s function . We derive a Menon-type identity using Klee’s function and a generalization of the gcd function. This identity generalizes an identity given by Y. Li and D. Kim (2017).
Hanspeter Kraft, Immanuel Stampfli (2013)
Annales de l’institut Fourier
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We show that every automorphism of the group of polynomial automorphisms of complex affine -space is inner up to field automorphisms when restricted to the subgroup of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension where all automorphisms are tame: . The methods are different, based on arguments from algebraic group actions.
Antonella Leone (2006)
Bollettino dell'Unione Matematica Italiana
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An automorphism a of a group G is called an artinian automorphism if for every strictly descending chain of subgroups of G there exists a positive integer such that for every . In this paper we show that in many cases the group of all artinian automorphisms of coincides with the group of all power automorphisms of .
Félix Cabello Sánchez (2004)
Studia Mathematica
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We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of is [algebraically] reflexive if and only if is *-isomorphic to . For purely atomic measures, we show that the group of automorphisms (or isometries) of is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism...
Wilhelm Kaup, Dmitri Zaitsev (2006)
Journal of the European Mathematical Society
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We present a large class of homogeneous 2-nondegenerate CR-manifolds , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence between domains , in extends to a global real-analytic CR-automorphism of . We show that this class contains -orbits in Hermitian symmetric spaces of compact type, where is a real form of the complex Lie group and has an open orbit that is a bounded symmetric domain of tube type. ...
Ryszard Jajte (2010)
Colloquium Mathematicae
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Let α be an isometric automorphism of the algebra of bounded linear operators in (p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].
Roman V. Bessonov, Janko Bračič, Michal Zajac (2011)
Studia Mathematica
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We study operators whose commutant is reflexive but not hyperreflexive. We construct a C₀ contraction and a Jordan block operator associated with a Blaschke product B which have the above mentioned property. A sufficient condition for hyperreflexivity of is given. Some other results related to hyperreflexivity of spaces of operators that could be interesting in themselves are proved.
Rolf Farnsteiner (2014)
Journal of the European Mathematical Society
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In this article we study the interplay between algebro-geometric notions related to -points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that -points give rise to a number of new invariants of the AR-quiver on one hand, and exploit combinatorial properties of AR-components to obtain information on -points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial...
Piotr Koszmider, Cristóbal Rodríguez-Porras (2016)
Fundamenta Mathematicae
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We investigate Banach space automorphisms focusing on the possibility of representing their fragments of the form for A,B ⊆ ℕ infinite by means of linear operators from into , infinite A×B-matrices, continuous maps from B* = βB∖B into A*, or bijections from B to A. This leads to the analysis of general bounded linear operators on . We present many examples, introduce and investigate several classes of operators, for some of them we obtain satisfactory representations and for...
Antonio J. Calderón Martín, Candido Martín González (2007)
Bollettino dell'Unione Matematica Italiana
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We study the Banach-Lie group of Lie automorphisms of a complex associative -algebra. Also some consequences about its Lie algebra, the algebra of Lie derivations of , are obtained. For a topologically simple , in the infinite-dimensional case we have implying . In the finite dimensional case is a direct product of and a certain subgroup of Lie derivations from to its center, annihilating commutators.
Luc Pirio, Francesco Russo (2014)
Annales de l’institut Fourier
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It has been previously established that a Cremona transformation of bidegree (2,2) is linearly equivalent to the projectivization of the inverse map of a rank 3 Jordan algebra. We call this result the “”. In this article, we apply it to the study of quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension 4 and 5.
Nikolay Nikolov, László Pyber (2011)
Journal of the European Mathematical Society
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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If is the minimal degree of a representation of the finite group , then for every subset of with we have . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if , then has a...
Vladimir Ya. Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We give a quasiconformal version of the proof for the classical Lindelof theorem: Let map the unit disk conformally onto the inner domain of a Jordan curve : Then is smooth if and only if arg has a continuous extension to . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
Dariusz Partyka (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Given a quasisymmetric automorphism of the unit circle we define and study a modification of the classical Poisson integral operator in the case of the unit disk . The modification is done by means of the generalized Fourier coefficients of . For a Lebesgue’s integrable complexvalued function on , is a complex-valued harmonic function in and it coincides with the classical Poisson integral of provided is the identity mapping on . Our considerations are motivated by...
G. Letac, J. Wesołowski (2011)
Bulletin de la Société Mathématique de France
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If the space of quadratic forms in is splitted in a direct sum and if and are independent random variables of , assume that there exist a real number such that and real distinct numbers such that for any in We prove that this happens only when , when can be structured in a Euclidean Jordan algebra and when and have Wishart distributions corresponding to this structure.
Tao Xu, Fang Zhou, Heguo Liu (2016)
Czechoslovak Mathematical Journal
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In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if is an automorphism of order four of a polycyclic group and the map defined by is surjective, then contains a characteristic subgroup of finite index such that the second derived subgroup is included in the centre of and is abelian, both and are abelian-by-finite. These results extend recent and classical results in...
Peteris Daugulis (2017)
Archivum Mathematicum
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The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having vertices and automorphism group cyclic of order , . As a special case we get graphs with vertices and cyclic automorphism groups of order . It can revive interest in related problems.
Cinzia Bisi, Jean-Philippe Furter, Stéphane Lamy (2014)
Journal de l’École polytechnique — Mathématiques
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We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.