Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=SFDMFbzCsH0&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Functional Analysis Lecture 12 2014 03 04 Boundedness of Hilbert Transform on Hardy Space (part 1)
Dyadic Whitney decomposition needed to extend characterization of Hardy space functions to higher dimensions. p-atoms: definition, have bounded Hardy space norm; p-atoms can also be used in place of atoms to define Hardy space. The Hilbert Transform is bounded from Hardy space to L^1: b
From playlist Course 9: Basic Functional and Harmonic Analysis
The complexification of a real vector space. The complexification of an operator on a real vector space. Every operator on a nonzero finite-dimensional real vector space has an invariant subspace of dimension 1 or 2. Every operator on an odd-dimensional real vector space has an eigenvalue.
From playlist Linear Algebra Done Right
Oscar Bandtlow: Spectral approximation of transfer operators
The lecture was held within the framework of the Hausdorff Trimester Program "Dynamics: Topology and Numbers": Conference on “Transfer operators in number theory and quantum chaos” Abstract:The talk will be concerned with the problem of how to approximate spectral data oftra
From playlist Conference: Transfer operators in number theory and quantum chaos
Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=BctaYoR9tOY&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=PBMyBVPRtKA&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
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
Jens Kaad: Exterior products of compact quantum metric spaces
Talk by Jens Kaad in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 24, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"
Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber
From playlist Actions of Tensor Categories on C*-algebras 2021
William B. Johnson: Ideals in L(L_p)
Abstract: I’ll discuss the Banach algebra structure of the spaces of bounded linear operators on ℓp and Lp := Lp(0,1). The main new results are 1. The only non trivial closed ideal in L(Lp), 1 ≤ p [is less than] ∞, that has a left approximate identity is the ideal of compact operators (joi
From playlist Analysis and its Applications
Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8
From playlist Dynamical Systems and Ordinary Differential Equations
Categorical aspects of vortices (Lecture 1) by Niklas Garner
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Math 131 092116 Properties of Compact Sets
Properties of compact sets. Compact implies closed; closed subsets of compact sets are compact; collections of compact sets that satisfy the finite intersection property have a nonempty intersection; infinite subsets of compact sets must have a limit point; the infinite intersection of ne
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Erez Lapid - 1/2 Some Perspectives on Eisenstein Series
This is a review of some developments in the theory of Eisenstein series since Corvallis. Erez Lapid (Weizmann Institute)
From playlist 2022 Summer School on the Langlands program
Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=-sfaHVFWBU8&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Eva Gallardo Gutiérrez: The invariant subspace problem: a concrete operator theory approach
Abstract: The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann's works in the fifties asking, in particular, if every bounded linear operator acting on an infinite dimensional separable Hilbert space has a non-
From playlist Analysis and its Applications
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