In mathematics, more specifically in functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly. Maurice René Fréchet was the first to use the term "Banach space" and Banach in turn then coined the term "Fréchet space."Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces. (Wikipedia).
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From playlist The Best of Futurism on YouTube
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See full video and explanation on @CuriousMarc
From playlist Soyuz Globus Mechanical Space Nav Computer
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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From playlist SciShow Space
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From playlist SciShow Space
The International Space Station continues an uninterrupted human presence in space as a test-bed for future exploration beyond low-Earth orbit and the only science lab in microgravity. This music video featuring the space station and its crews is set to the song "World" by recording artist
From playlist Real Space Stations - YouTube Space Lab with Liam & Brad
Some 20+ year old problems about Banach spaces and operators on them – W. Johnson – ICM2018
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From playlist Analysis & Operator Algebras
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Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
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This workshop - organised under the auspices of the Isaac Newton Institute on “Approximation, sampling and compression in data science” — brings together leading researchers in the general fields of mathematics, statistics, computer science and engineering. About the event The workshop ai
From playlist Mathematics of data: Structured representations for sensing, approximation and learning
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From playlist Analysis & Operator Algebras
William B. Johnson: Ideals in L(L_p)
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From playlist Analysis and its Applications
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From playlist HIM Lectures: Junior Trimester Program "Randomness, PDEs and Nonlinear Fluctuations"
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From playlist SciShow Space
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From playlist SciShow Space
2020.05.28 Andrew Stuart - Supervised Learning between Function Spaces
Consider separable Banach spaces X and Y, and equip X with a probability measure m. Let F: X \to Y be an unknown operator. Given data pairs {x_j,F(x_j)} with {x_j} drawn i.i.d. from m, the goal of supervised learning is to approximate F. The proposed approach is motivated by the recent su
From playlist One World Probability Seminar
Lecture with Ole Christensen. Kapitler: 00:00 - Banach Spaces; 06:30 - Cauchy Sequences; 12:00 - Def: Banach Space; 15:45 - Examples; 17:15 - C[A,B] Is Banach With Proof; 36:30 - Ex: Sequence Space L^1(N); 46:45 - Sequence Space L^p(N);
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Minerva Lectures 2013 - Assaf Naor Talk 1: An introduction to the Ribe program
For more information, please see: http://www.math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-i-introduction-ribe-program
From playlist Minerva Lectures - Assaf Naor
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From playlist SciShow Space
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From playlist What is Space? YouTube Space Lab with Liam and Brad
Christina Sormani: A Course on Intrinsic Flat Convergence part 3
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From playlist HIM Lectures 2015