Von Neumann algebras | Operator algebras | Hilbert space

Calkin correspondence

In mathematics, the Calkin correspondence, named after mathematician John Williams Calkin, is a bijective correspondence between two-sided ideals of bounded linear operators of a separable infinite-dimensional Hilbert space and Calkin sequence spaces (also called rearrangement invariant sequence spaces). The correspondence is implemented by mapping an operator to its singular value sequence. It originated from John von Neumann's study of symmetric norms on matrix algebras. It provides a fundamental classification and tool for the study of two-sided ideals of compact operators and their traces, by reducing problems about operator spaces to (more resolvable) problems on sequence spaces. (Wikipedia).

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Planes and vectors

What is the connection between vectors and equations of planes? Find out here! Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/ZTQ0pvOq1q

From playlist Introduction to Vectors

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Duality Argument

In this video, I present a very classical example of a duality argument: Namely, I show that T^T is one-to-one if and only if T is onto and use that to show that T is one-to-one if and only if T^T is onto. This illustrates the beautiful interplay between a vector space and its dual space,

From playlist Dual Spaces

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23 Algebraic system isomorphism

Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.

From playlist Abstract algebra

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What are parallel lines and a transversal

๐Ÿ‘‰ Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What are the Angle Relationships for Parallel Lines and a Transversal

๐Ÿ‘‰ Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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Proving Parallel Lines with Angle Relationships

๐Ÿ‘‰ Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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Parallel and Perpendicular Lines and Planes

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From playlist Parallel and Perpendicular Lines

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[SoME1] Listing the Rationals Using Continued Fractions

This video was produced for the #SoME1 exposition in 2021. See the full series here: https://www.youtube.com/playlist?list=PLWhQvrZCGE5IHCqO21zo75NEGOSTANmQN This video follows from a talk I gave in August 2021. The early elements of my method are attributed to work done by Jack Graver

From playlist Summer of Math Exposition Youtube Videos

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The Hitchhiker's Killer: Pee Wee Gaskins | Real Crime

Make sure you subscribe to get your regular crime fix: youtube.com/c/RealCrime Psychologists and criminology experts analyse the personality of Donald Gaskins Jr. The man, who earned the nickname `meanest man in America', boasted about his private graveyard for victims. He was put to deat

From playlist Our Favourite Videos

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Lines: Cartesian to parametric form

How to convert a Cartesian form of a line to a parametric form. An example is discussed. Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link)

From playlist Introduction to Vectors

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Where Are The Worlds In Many Worlds?

Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Many Worlds interpretation of quantum mechanics proposes that every time a quantum event gets decided, the universe splits so that every possible outcome really does occur. But where exactly a

From playlist Many Worlds and the Multiverse Explained!

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How To Determine If Two Lines are Parallel to Apply Angle Theorems

๐Ÿ‘‰ Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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How Vacuum Decay Would Destroy The Universe

Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime The universe is going to end. But of all the possible ends of the universe vacuum decay would have to be the most thorough - because it could totally rewrite the laws of physics. Today I hope

From playlist The End of The Universe!

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How to Communicate Across the Quantum Multiverse

Check Out Megawow on PBS Kids: https://youtu.be/meU4f31gqYI In the Many Worlds interpretation of quantum mechanics, the universal wavefunction is the reality, encompassing all possible histories and futures and all exist. But we are only sensitive to a slice of the wavefunction correspon

From playlist Many Worlds and the Multiverse Explained!

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What If Charge is NOT Fundamental?

Check Out Subcultured's Anime Episode on PBS Voices: https://youtu.be/oSCj8H4TGTo Take the Space Time Fan Survey Here: https://forms.gle/wS4bj9o3rvyhfKzUA PBS Member Stations rely on viewers like you. To support your local station, go to:http://to.pbs.org/DonateSPACE If you've studied a

From playlist The Standard Model Lagrangian Playlist

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How the Higgs Mechanism Give Things Mass

Take the Space Time Fan Survey Here: https://forms.gle/wS4bj9o3rvyhfKzUA PBS Member Stations rely on viewers like you. To support your local station, go to:http://to.pbs.org/DonateSPACE Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Ferm

From playlist The Standard Model Lagrangian Playlist

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Tropical Geometry - Lecture 2 - Curve Counting | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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Is ACTION The Most Fundamental Property in Physics?

Learn More About NordVPN at: https://nordvpn.com/spacetime Itโ€™s about time we discussed an obscure concept in physics that may be more fundamental than energy and entropy and perhaps time itself. Thatโ€™s right - the time has come for Action. Sign Up on Patreon to get access to the Space

From playlist The Standard Model Lagrangian Playlist

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Lines and a Transversal - How To Label Special Angle Relationships

๐Ÿ‘‰ Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral

From playlist Parallel Lines and a Transversal

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Ash, Vito Cornelius, and Bilbo - Still Untitled: The Adam Savage Project - 6/23/20

We recall the amazing careers of actor Ian Holm and director Joel Schumacher, whose works hold special places in the pop culture pantheon. Adam, Will, and Norm also talk about great character actors whose appearance and performances elevate the films they show up in, and give a few recomme

From playlist The Adam Savage Project

Related pages

Sequence space | Singular trace | Compact operator | John Williams Calkin | Singular value | Hilbert space | Schatten class operator | Linear algebra | Lp space | Ideal (ring theory) | Finite-rank operator | Braโ€“ket notation | Lorentz space | John von Neumann