Banach spaces | Functional analysis | Norms (mathematics) | Normed spaces
In the mathematical field of functional analysis, the space denoted by c is the vector space of all convergent sequences of real numbers or complex numbers. When equipped with the uniform norm: the space becomes a Banach space. It is a closed linear subspace of the space of bounded sequences, , and contains as a closed subspace the Banach space of sequences converging to zero. The dual of is isometrically isomorphic to as is that of In particular, neither nor is reflexive. In the first case, the isomorphism of with is given as follows. If then the pairing with an element in is given by This is the Riesz representation theorem on the ordinal For the pairing between in and in is given by (Wikipedia).
Introduction to the C programming language. Part of a larger series teaching programming. See http://codeschool.org
From playlist The C language
Introduction to the C programming language. Part of a larger series teaching programming. See http://codeschool.org
From playlist The C language
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
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Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Special Relativity
A01 An introduction to a series on space medicine
A new series on space medicine.
From playlist Space Medicine
From playlist CG animations
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From playlist Science Unplugged: Physics
Color Quantization (almost) done! -- Watch live at https://www.twitch.tv/simuleios
From playlist Space trees and stuff
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Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an
From playlist New perspectives on K- and L-theory
Part III: Linear Algebra, Lec 2: Spanning Vectors
Part III: Linear Algebra, Lecture 2: Spanning Vectors Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Calculus of Complex Variables
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In this lesson we cover the spacetime product of a Bivector and a vector as presented in section 3.3.1 of our topic paper. Our topic paper can be found at: https://arxiv.org/abs/1411.5002 Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software
From playlist QED- Prerequisite Topics
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From playlist Special and General Relativity
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In this video, we provide further properties of the derived category of an abelian category. Along the way we discuss slice categories and filtered colimits. This is the fifth video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our pub
From playlist Higher Algebra
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Talk by Matthew Kennedy in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 5, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
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From playlist Higher Algebra
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PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE (ONLINE) ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Mahan M J (TIFR, Mumbai) DATE & TIME: 01 March 2021 to 12 March 2021 VENUE: Online Due to the ongoing COVID pandemic, the meeting will
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Metric Spaces - Lectures 15 & 16: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 8th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces