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The Bishop–Phelps–Bollobás theorem for operators

2008

AbstractWe prove the Bishop–Phelps–Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop–Phelps–Bollobás theorem holds for operators from ℓ1 into Y. Several examples of classes of such spaces are provided. For instance, the Bishop–Phelps–Bollobás theorem holds when the range space is finite-dimensional, an L1(μ)-space for a σ-finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.

Discrete mathematicsPure mathematicsMathematics::Functional AnalysisApproximation propertyEberlein–Šmulian theoremBanach spaceNorm attainingBishop–Phelps theoremUniform boundedness principleUniform convexityInterpolation spaceOperatorClosed graph theoremReflexive spaceBishop–Phelps theoremAnalysisMathematicsJournal of Functional Analysis
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Identities of *-superalgebras and almost polynomial growth

2015

We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.

Discrete mathematicsPure mathematicsPolynomialAlgebra and Number TheoryMathematics::Commutative Algebraalmost polynomial growthgraded involution010102 general mathematicsZero (complex analysis)Field (mathematics)010103 numerical & computational mathematics01 natural sciencesMatrix polynomialSquare-free polynomialSimple (abstract algebra)polynomial identity0101 mathematicsAlgebraically closed fieldCharacteristic polynomialMathematics
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A note on the closed graph theorem

1977

Discrete mathematicsUniform boundedness principleDual spaceGeneral MathematicsBanach spaceClosed graph theoremLp spaceReflexive spaceQuotient space (linear algebra)Complete metric spaceMathematicsArchiv der Mathematik
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WQ*-algebras of measurable operators

2012

Every C*-algebra \(\mathfrak{A}\) has a faithful *-representation π in a Hilbert space \(\mathcal{H}\). Consequently it is natural to pose the following question: under which conditions, the completion of a C*-algebra in a weaker than the given one topology, can be realized as a quasi *-algebra of operators? The present paper presents the possibility of extending the well known Gelfand — Naimark representation of C*-algebras to certain Banach C*-modules.

Discrete mathematicsmonotone closedPure mathematicsApplied MathematicsGeneral MathematicsHilbert spacemodular representation.C*-algebraCQ*-algebrasymbols.namesakeSettore MAT/05 - Analisi MatematicaGelfand–Naimark theoremsymbolsCQ*-algebra; WQ*-algebra; Monotone closed; Modular representationlcsh:QAlgebra over a fieldlcsh:ScienceRepresentation (mathematics)Topology (chemistry)WQ*-algebraMathematicsIndian Journal of Pure and Applied Mathematics
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Counterexamples to the Algebraic Closed Graph Theorem

1982

Discrete mathematicssymbols.namesakeAlgebraic graph theoryGeneral MathematicsPerfect graphsymbolsGraph minorPerfect graph theoremClosed graph theoremRobertson–Seymour theoremPlanar graphMathematicsExtremal graph theoryJournal of the London Mathematical Society
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Closeness and distance through the agentive authorial voice: construing credibility in promotional discourse.

2020

Credibility is a function associated with promotional genres and persuasion, and a powerful marketing concept (Eisend, 2006; Ming, 2006) which provides trustworthiness about the quality of products or services offered by hotels (Suau-Jiménez, 2012a, 2019). It is partly attained through the hotel‘s self-mentioning in websites. When this self-mentioning is agentive with action verbs, the main instantiation is the pronoun we, projecting closeness and assertiveness. However, this self-representation is also construed with depersonalized realizations like the hotel‘s proper name, other nominalizations or even pronouns like it and they, which provide attenuating aspects and create a sense of dist…

DistanceAgentive self mentioningCredibilityPersuasionAttenuationClosenessAnàlisi del discursHotel websites:8- Lingüística y literatura [CDU]
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Double-Blind Study on the Effects of Steroids on Severe Closed Head Injury

1976

The results of a double-blind study on the effects of a low dose and a high dose of dexamethasone on severe closed head injury are presented. The steroid, particularly in high dose, reduced mortality, improved the neurologic course and the final outcome. Timing of steroid administration is of great importance.

Double blind studySevere head injurybusiness.industryBrain edemaAnesthesiaClosed head injuryHead injuryLow doseMedicinebusinessmedicine.diseaseDexamethasonemedicine.drug
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Voters’ preferences and electoral systems: the EuroVotePlus experiment in Italy

2016

Motivated by the need to understand voting behaviour under different electoral rules, Laslier et al. (Eur Union Polit, 16(4):601–615, 2015) have conducted an online experiment, the EuroVotePlus experiment, focusing on the effects of the different rules adopted to elect members of the European parliament on voters’ behaviour. The experiment took place in several European countries in the 3 weeks before the 2014 elections for the European Parliament. This paper focuses on the Italian data. Firstly, we show that the behaviour of Italian respondents is consistent with the empirical findings at the European level. Then, we exploit the change from open list to closed list elections implemented in…

Economics and EconometricsEuropean levelOpen listSECS-P/02 - POLITICA ECONOMICASociology and Political ScienceExploitParliamentmedia_common.quotation_subjectClosed listClosed listEuropean Parliament Election Open list Closed list Voting rulesOpen ListVoting0502 economics and business050602 political science & public administrationEconomics050207 economicsSECS-P/01 - ECONOMIA POLITICASettore SECS-P/01 - Economia Politicamedia_commonEuropean Parliament Election05 social sciencesEuropean Parliament Election; Open List; Close List; Voting Rules;European Parliament Election; Open List; Close List; Voting RulesClose List0506 political scienceEconomyPolitical economyInternational political economySettore SECS-P/03 - Scienza delle FinanzeVoting RulesFinance
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The closed-form solution for a family of four-dimension nonlinear MHDS

2008

In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externa…

Economics and EconometricsNonlinear systemState variableMathematical optimizationControl and OptimizationEndogenous growth theoryApplied MathematicsIntertemporal optimizationClosed-form expressionMathematical economicsExternalityHamiltonian (control theory)MathematicsJournal of Economic Dynamics and Control
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Vacuum induced berry phase: Theory and experimental proposal

2003

We investigate quantum effects in geometric phases arising when a two-level system is interacting with a quantized electromagnetic field. When the system is adiabatically driven along a closed loop in the parameter space, signatures of the field quantization are observable in the geometric phase. We propose a feasible experiment to measure these effects in cavity QED and also analyse the semi-classical limit, recovering the usual Berry phase results.

Electromagnetic fieldPhysicsJaynes–Cummings modelVacuumGround stateMathematical transformationObservableParameter spaceComputational geometryAtomic and Molecular Physics and OpticsClosed loop control systemQuantization (physics)Mathematical operatorGeometric phaseConvergence of numerical methodQuantum electrodynamicsQuantum mechanicsElectromagnetic fieldBerry connection and curvatureFunctionClosed loopLight polarizationJournal of Modern Optics
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