On the Jordan model operators
Hari Bercovici (1977)
Studia Mathematica
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Hari Bercovici (1977)
Studia Mathematica
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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...
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...
M. Mateljević (1975)
Matematički Vesnik
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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.
Marcell Gaál (2020)
Commentationes Mathematicae Universitatis Carolinae
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The binary operation , called Jordan triple product, and its variants (such as e.g. the sequential product or the inverted Jordan triple product ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.
Jean-Marie De Koninck, Nicolas Doyon, A. Arthur Bonkli Razafindrasoanaivolala, William Verreault (2020)
Archivum Mathematicum
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A positive integer is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number .
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...
Mohammad Ashraf, Nazia Parveen, Bilal Ahmad Wani (2017)
Communications in Mathematics
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Let be the triangular algebra consisting of unital algebras and over a commutative ring with identity and be a unital -bimodule. An additive subgroup of is said to be a Lie ideal of if . A non-central square closed Lie ideal of is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on , every generalized Jordan triple higher derivation of into is a generalized higher derivation of into . ...
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. ...
Haixian Chen, Ying Wang (2018)
Czechoslovak Mathematical Journal
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Let be a simple strange Lie superalgebra over the complex field . In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but is an exception....
Mohammad Ashraf, Shakir Ali, Bilal Ahmad Wani (2018)
Communications in Mathematics
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Let be an infinite-dimensional complex Hilbert space and be a standard operator algebra on which is closed under the adjoint operation. It is shown that every nonlinear -Lie higher derivation of is automatically an additive higher derivation on . Moreover, is an inner -higher derivation.
Ioana Ghenciu (2023)
Commentationes Mathematicae Universitatis Carolinae
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We introduce the definition of -limited completely continuous operators, . The question of whether a space of operators has the property that every -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using -limited completely continuous evaluation operators.
Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)
Archivum Mathematicum
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In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators for which there exists a fundamental decomposition of the Krein space with and invariant under .
Mohammad Ashraf, Mohammad Aslam Siddeeque, Abbas Hussain Shikeh (2024)
Czechoslovak Mathematical Journal
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Let be a noncommutative prime ring equipped with an involution ‘’, and let be the maximal symmetric ring of quotients of . Consider the additive maps and . We prove the following under some inevitable torsion restrictions. (a) If and are fixed positive integers such that for all and for all , then . (b) If for all , then . Furthermore, we characterize Jordan left -centralizers in semiprime rings admitting an anti-automorphism . As applications, we find the...
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).
Ioana Ghenciu, Paul Lewis (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space , as well as the complementation of the space of w*-w compact operators in the space of w*-w operators from X* to Y.
Sara Chehrazi, Ali Reza Salemkar (2016)
Czechoslovak Mathematical Journal
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A subalgebra of a finite dimensional Lie algebra is said to be a -subalgebra if there is a chief series of such that for every , we have or . This is analogous to the concept of -subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its -subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.
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...
Xinfeng Liang, Feng Wei, Ajda Fošner (2019)
Czechoslovak Mathematical Journal
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Let be a commutative ring, be a generalized matrix algebra over with weakly loyal bimodule and be the center of . Suppose that is an -bilinear mapping and that is a trace of . The aim of this article is to describe the form of satisfying the centralizing condition (and commuting condition ) for all . More precisely, we will revisit the question of when the centralizing trace (and commuting trace) has the so-called proper form from a new perspective. Using the aforementioned...