Extreme Points in Quotients of Operator Algebras

1988 ◽  
pp. 67-91
Author(s):  
Kenneth R. Davidson ◽  
Timothy G. Feeman ◽  
Allen L. Shields
Keyword(s):  
Operator Algebras ◽  
Extreme Points

scholarly journals ON THE ORDER STRUCTURE OF REPRESENTABLE FUNCTIONALS

2017 ◽  
Vol 60 (2) ◽  
pp. 289-305 ◽  
Author(s):  
ZSIGMOND TARCSAY ◽  
TAMÁS TITKOS
Keyword(s):  
Operator Algebras ◽  
Extreme Points ◽  
Positive Operators ◽  
Order Structure ◽  
Sufficient Condition ◽  
Lebesgue Decomposition ◽  
Decomposition Theory ◽  
The One ◽  
Order Intervals ◽  
Complete Analogy

AbstractThe main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on *-algebras. We describe the extreme points of order intervals, and give a non-trivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim, we offer a suitable approach to the Lebesgue decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the decomposition, and solve the infimum problem over certain operator algebras.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

Extreme Points and Majorization: Economic Applications

2020 ◽  
Author(s):  
Andreas Kleiner ◽  
Benny Moldovanu ◽  
Philipp Strack
Keyword(s):  
Extreme Points ◽  
Economic Applications

scholarly journals W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Nilpotent Orbit ◽  
Vertex Operator Algebras ◽  
Flavor Symmetries ◽  
Conformal Embedding

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

scholarly journals A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

scholarly journals Investigation of ancestral alleles in the Bovinae subfamily

BMC Genomics ◽  
2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Maulana M. Naji ◽  
Yuri T. Utsunomiya ◽  
Johann Sölkner ◽  
Benjamin D. Rosen ◽  
Gábor Mészáros
Keyword(s):  
Extreme Points ◽  
Genetic Mutation ◽  
Zebu Cattle ◽  
Ancestral State ◽  
Initial State ◽  
High Count ◽  
Environmental Pressures ◽  
Ancestral States ◽  
Productive Traits ◽  
Species Specific

Abstract Background In evolutionary theory, divergence and speciation can arise from long periods of reproductive isolation, genetic mutation, selection and environmental adaptation. After divergence, alleles can either persist in their initial state (ancestral allele - AA), co-exist or be replaced by a mutated state (derived alleles -DA). In this study, we aligned whole genome sequences of individuals from the Bovinae subfamily to the cattle reference genome (ARS.UCD-1.2) for defining ancestral alleles necessary for selection signatures study. Results Accommodating independent divergent of each lineage from the initial ancestral state, AA were defined based on fixed alleles on at least two groups of yak, bison and gayal-gaur-banteng resulting in ~ 32.4 million variants. Using non-overlapping scanning windows of 10 Kb, we counted the AA observed within taurine and zebu cattle. We focused on the extreme points, regions with top 0. 1% (high count) and regions without any occurrence of AA (null count). High count regions preserved gene functions from ancestral states that are still beneficial in the current condition, while null counts regions were linked to mutated ones. For both cattle, high count regions were associated with basal lipid metabolism, essential for survival of various environmental pressures. Mutated regions were associated to productive traits in taurine, i.e. higher metabolism, cell development and behaviors and in immune response domain for zebu. Conclusions Our findings suggest that retaining and losing AA in some regions are varied and made it species-specific with possibility of overlapping as it depends on the selective pressure they had to experience.

scholarly journals Integrable and Chaotic Systems Associated with Fractal Groups

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon
Keyword(s):  
Operator Algebras ◽  
Probabilistic Approach ◽  
Schur Complement ◽  
Automata Theory ◽  
Random Schrödinger Operators ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Von Neumann ◽  
Intermediate Growth ◽  
Quasi Crystals

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

Z2k-code vertex operator algebras

2021 ◽  
Vol 573 ◽  
pp. 451-475
Author(s):  
Hiromichi Yamada ◽  
Hiroshi Yamauchi
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras
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