Operator theory

Operator theory

In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis. If a collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory. (Wikipedia).

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Operators in Quantum Mechanics

We discuss some general ideas about operators in quantum mechanics.

From playlist Quantum Mechanics Uploads

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Ever heard of Quantum Operators and Commutators? (Explained for Beginners)!

What is a quantum operator? And just how useful are quantum commutators? Find out how they help us understand the Ehrenfest Theorem! Hi everyone, I'm back with a new video! This time it's the first in a two-part mini-series on one of the coolest theorems in quantum mechanics - Ehrenfest's

From playlist Quantum Physics by Parth G

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Functions, operators, and linearity: the language of abstract math (#SoME1)

Mathematicians and physicists often use abstract notation and terminology to reason about and describe problems at a level above the explicit details of the problem, but often take for granted that everyone already understands what they're doing and why. This video gives a short explanati

From playlist Summer of Math Exposition Youtube Videos

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RNT1.4. Ideals and Quotient Rings

Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.

From playlist Abstract Algebra

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Adjoint / Daggered Operators in Quantum Mechanics

In this video, we will explain adjoint operators in quantum mechanics. First of all, for any operator A, we can define its adjoint, A-dagger, via this equation. The idea behind this is, that while operators in quantum mechanics usually act towards the right, adjoint operators act to the le

From playlist Quantum Mechanics, Quantum Field Theory

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Definition of a group Lesson 24

In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el

From playlist Abstract algebra

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Schemes 46: Differential operators

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin

From playlist Algebraic geometry II: Schemes

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Linear Transformations: Onto

Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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Determinant of an Operator and of a Matrix

Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.

From playlist Linear Algebra Done Right

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Conformal Bootstrap (Lecture - 01) by Luis Fernando Alday

Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018 DATE:08 January 2018 to 18 January 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology is a pan-Asian collaborative effort of high energy theori

From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

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Symmetries in QFT and Their Relationship With Category Theory (Lecture 1) by Lakshya Bhardwaj

INFOSYS-ICTS STRING THEORY LECTURES SYMMETRIES IN QFT AND THEIR RELATIONSHIP WITH CATEGORY THEORY SPEAKER Lakshya Bhardwaj (Mathematical Institute, University of Oxford) DATE & TIME 10 October 2022 to 12 October 2022 VENUE Madhava Lecture Hall (Hybrid) Lecture 1: 10 October 2022 at 3:30 p

From playlist Infosys-ICTS String Theory Lectures

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Secondary products in SUSY QFT by Tudor Dimofte

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

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Symmetry in Quantum Gravity by Hirosi Ooguri

DATE: 15 January 2018, 16:00 to 17:30 VENUE: Ramanujan Lecture Hall, ICTS Bangalore General relativity and quantum mechanics were crowning achievements of physics in the 20th century, and their unification has been left as our homework in the 21st century. Superstring theory is our best

From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

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PiTP-Supersymmetric Grand Unification, Part 2 - Stuart Raby

PiTP-Supersymmetric Grand Unification, Part 2 Stuart Raby The Ohio State University July 17, 2008

From playlist PiTP 2008

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Index Theory, survey - Stephan Stolz [2018]

TaG survey series These are short series of lectures focusing on a topic in geometry and topology. May_8_2018 Stephan Stolz - Index Theory https://www3.nd.edu/~math/rtg/tag.html (audio fixed)

From playlist Mathematics

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Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry (3/4)

Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019

From playlist Slava Rychkov - Random Field Ising Model and Parisi-Sourlas Supersymmetry

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Category Theory 2.1: Functions, epimorphisms

Functions, epimorphisms

From playlist Category Theory

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Differential operator | Commutator | Functional analysis | Functional calculus | Self-adjoint operator | Integral operator | Diagonalizable matrix | *-algebra | Spectral theorem | Topology | Fredholm operator | Theorem | Toeplitz operator | Invariant subspace | Resolvent formalism | Douglas' lemma | Map (mathematics) | Operator (mathematics) | Diagonal matrix | Umbral calculus | Perron–Frobenius theorem | Algebra over a field | Singular value decomposition | Unitary operator | Banach algebra | Partial isometry | C*-algebra | Multiplication operator | Operator algebra | Fredholm theory | Normal operator | Mathematics | Unbounded operator | Function space | Ordered vector space | Von Neumann algebra | Bergman space | Holomorphic function | Schur decomposition | Semigroup with involution | Spectral radius | Unitary matrix | Compact operator | Shift operator | Integral equation | Hilbert space | Complex number | Contraction mapping | Hardy space | Canonical form | Hermitian adjoint | Matrix (mathematics) | Eigendecomposition of a matrix | Continuous functional calculus | Spectral theory