LAB LOGA page on LabLog, a review site (not the lab's official page)
Functional Analysis and Operator Algebras Lab
Machine-translated · View original
Research that broadens the analysis of noncommutative quantities, building on operator algebra theory.
AboutAbout the lab
Broadening the analysis of noncommutative quantities
Prof. Ueda studies noncommutative analysis broadly, building on operator algebra theory.
Operator algebra theory demands both the power of algebra to handle noncommutativity and the power of analysis to overcome infinite-dimensionality.
The lab also conducts research related to harmonic analysis, probability theory, and ergodic theory, aiming to contribute to the analysis of noncommutative quantities based on operator algebras.
Key terms
- Operator algebra
- A collection of linear transformations (operators) on a Hilbert space, set up so that they can be added and multiplied.
- Noncommutative
- A property whereby changing the order of multiplication changes the result. It occurs, for example, in matrix multiplication.
- Ergodic theory
- A field that uses the ideas of probability (measure) to study the long-term average behavior of dynamical systems.
- Free probability theory
- A theory that treats noncommutative quantities in the manner of probability theory, using a notion of independence called "freeness."
ResearchResearch themes
The lab studies a relatively wide range of topics, building on operator algebra theory. It is currently moving somewhat away from topics specific to operator algebra theory and exploring ways to help broaden the field's reach.
*Illustrative imageNoncommutative Analysis Built on Operator Algebra Theory
The real appeal of operator algebra theory lies in wrestling with noncommutative phenomena and overcoming infinite-dimensionality. Noncommutativity calls for algebraic formulation and handling, while infinite-dimensionality calls for the power of analysis, and this combination is what makes the field interesting.
*Illustrative imageResearch in Harmonic Analysis, Probability Theory, and More
In addition to problems specific to operator algebra theory, the lab conducts research related to harmonic analysis, probability theory, and ergodic theory. Free probability theory is also one of its research themes.
*Illustrative imageBroadening the Reach of Operator Algebra Theory
The lab has studied von Neumann algebras, quantum groups, subfactors, random matrices, and noncommutative function spaces. It is now exploring directions that move somewhat away from topics specific to operator algebra theory and broaden the field's reach.
MembersFaculty
- ProfessorYoshimichi Ueda
VoicesStudent voices
Ratings and reviews reflect the experiences of individual current or former students, not the lab's official views. Whether a lab has reviews, or how many, says nothing about the lab itself.
Students who take part in an interview may receive a thank-you gift worth ¥1,000, regardless of what they say.
Student ratings (0 students)
--
--
--
--
--
--
Student voices answer questions like these
- What's great about this lab?
- What did you learn after joining?
- What's the vibe, and what is the professor like?
- Who is this lab for?
- Where do graduates go?
Your experience can help younger students choose their lab. Your name won't be shown.
Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Functional Analysis and Operator Algebras Lab
Arano LabSchool of Science, Department of MathematicsQuantum groups in the operator-algebraic sense, as group str…
Representation Theory and Infinite-Dimensional Integrable Systems LabSchool of Science, Department of MathematicsQuantum groups and their representation theory. Quantum grou…
Fourier Analysis, Partial Differential Equations, and Fluid Dynamics LabSchool of Science, Department of MathematicsNavier–Stokes equations for incompressible viscous fluids an…
Ring Theory and Representation Theory LabSchool of Science, Department of MathematicsRepresentation theory of algebras; quasi-hereditary algebras…The information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Mathematics lecture at the Helsinki University of Technology” Tungsten / Public domain (cropped)
- Noncommutative Analysis Built on Operator Algebra Theory: “Mathematics (cryptography) on a blackboard” David Malone / CC BY 4.0 (cropped)
- Research in Harmonic Analysis, Probability Theory, and More: “Oscilloscope sine square” Xato / Public domain (cropped)
- Broadening the Reach of Operator Algebra Theory: “(Diagram) Plate 3. Mathematical and Geometrical problems. (IA dr diagram-plate-3-mathematical-and-geometrical-problems-12190036)” Heck, Johann Georg, -1857 Henry Winkles / Public domain (cropped)
- Related lab (表現論・作用素環論
（荒野 悠輝） ): “Mathematics lecture notes, Mathematical analysis, Linear algebra, Rostov-on-Don, Russia” Vyacheslav Argenberg / CC BY 4.0 (cropped) - Related lab (表現論・
無限可積分系 （林 孝宏） ): “Dynkin diagram Dn” Rogilbert / Public domain (cropped) - Related lab (フーリエ解析・偏微分方程式・流体力学
（寺澤 祐高） ): “Flow separation” Jaganath at English Wikipedia / CC BY-SA 3.0 (cropped) - Related lab (環論・
表現論 （塚本 真由） ): “Combined group axiom commutative diagram” Struoc / CC BY-SA 4.0 (cropped)
About LabLog
LabLog is a lab review app for students only. Student members at each university interview students in labs and publish what they say. Student voices can only be read by students who sign up with a university email address. Operated by bestiee Inc.
Learn more about LabLog ↗Search engines and AI may reference the basic lab info and rating summaries on this page and the description of LabLog. Student voices are for student members only. Automated collection by programs (scraping, or input to or training of AI) is prohibited under Article 8 of the Terms of Service. If you need data for research or analysis, please contact us.