Topics in Functional Analysis and Algebra.

Cover -- Title page -- Contents -- Preface -- Tracial and Arens algebras associated with finite von Neumann algebras -- 1. Introduction -- 2. Main results -- References -- A dichotomy property for the graphs of monomials -- 1. Motivation -- 2. Dichotomy property for monomials -- 3. A big-graph property -- References -- Characterization conditions and the numerical index -- 1. Introduction -- 2. Characterization conditions and numerical index -- 3. Computing the numerical index -- References -- On generalized localization of Fourier inversion for distributions -- 1. Introduction -- 2. Notation and Definitions -- 3. Main results -- 4. On estimates of smoothed kernel -- 5. Proof of Theorem 3.1 -- 6. Preliminary propositions for Theorem 3.2 -- 7. On negative Riesz means of ₂ functions -- 8. Proof of Theorem 3.2 -- References -- Derivations, local and 2-local derivations on algebras of measurable operators -- 1. Introduction -- 2. Locally measurable operators affiliated with von Neumann algebras -- 3. Derivations on algebras of measurable operators for type I von Neumann algebras -- 4. Derivations on algebras of measurable operators for arbitrary von Neumann algebras -- 5. Local derivations on algebras of measurable operators -- 6. 2-Local derivations on algebras of measurable operators -- Acknowledgement -- References -- A survey on local and 2-local derivations on C*- and von Neuman algebras -- 1. Introduction -- 2. Local derivations on C*-algebras -- 3. Hochschild cohomology of C*-algebras and local n-cocycles -- 4. Local triple derivations -- 5. Some comments on automatic continuity -- 6. 2-local derivations on von Neumann algebras -- References -- Cohomology of Jordan triples via Lie algebras -- 1. Introduction -- 2. Jordan triples and TKK Lie algebras -- 3. Cohomology of Lie algebras with involution -- 4. Cohomology of Jordan triples.

5. Examples -- 6. Proofs of Theorems 2.3 and 5.5 -- References -- Extreme boundary of the space semi-additive functionals on the three-point set -- 1. Introduction -- 2. Preliminaries -- 3. The main result -- Acknowledgment -- References -- Algebras with genetic realization and corresponding evolutionary population dynamics -- 1. Introduction -- 2. Preliminaries: Ergodicity of qso and paper-rock-scissors games -- 3. Qso and corresponding algebras with genetic realization -- 4. RPS Algebras of any dimension -- References -- Quadratic homeomorphisms of the two-dimensional simplex and their trajectories -- 1. Introduction -- 2. Main result -- Acknowledgement -- References -- On universal representations and universal enveloping locally C*-algebras for locally JB-algebras -- 1. Introduction -- 2. Preliminaries -- 3. Locally homomorphic locally JB-algebras of type Λ -- 4. Universal representations of locally JB-algebras and their universal locally C*-algebra envelops -- References -- Complex powers of the Schrödinger operator with singular potential -- 1. Introduction -- 2. Proof of the Theorem 1 -- 3. Proof of the Theorem 2 -- Description of solvable Leibniz algebras with four-dimensional nilradical -- 1. Introduction. -- 2. Preliminaries. -- References -- On classification problem of Loday algebras -- 1. Introduction -- 2. Loday diagram -- 3. Leibniz algebras: Structural Theory -- 4. Semisimple case -- 5. Generalizations -- 6. Approaches applied: Classification of complex filiform Leibniz algebras -- Acknowledgements -- References -- On the classification of left-symmetric dialgebras -- Introduction -- 1. Left-symmetric algebras and dialgebras -- 2. Classification of two dimensional left-symmetric dialgebras -- Acknowledgements -- References -- Invitation to research of new mathematics from biology: Evolution algebras -- 1. Project objectives.

2. Background -- 3. Preliminary research -- 4. Proposed open research topics -- Acknowledgments -- References -- Back Cover.

The USA-Uzbekistan Conference on Analysis and Mathematical Physics, focusing on contemporary issues in dynamical systems, mathematical physics, operator algebras, and several complex variables, was hosted by California State University, Fullerton, from May 20-23, 2014. The main objective of the conference was to facilitate scientific communication and collaboration between mathematicians from the USA and Uzbekistan. This volume contains the proceedings of the Special Session on Algebra and Functional Analysis. The theory of operator algebras is the unified theme for many papers in this volume. Out of four extensive survey papers, two cover problems related to derivation of various algebras of functions. The other two surveys are on classification of Leibniz algebras and on evolution algebras. The sixteen research articles are devoted to certain analytic topics, such as minimal projections with respect to numerical radius, functional equations and discontinuous polynomials, Fourier inversion for distributions, Schrödinger operators, convexity and dynamical systems.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.