Warning: These are links to externals lists, not all of which are updated regularly by their owners. Unfortunately, this means it is the reader's responsibility to investigate whether particular problems remain open.
American Institute of Mathematics (AIM) Workshop Problem List
List of Open Problems on Hilbert C*-Modules, maintained by Michael Frank.
AIM Workshop on the Kadison-Singer Problem, September 2006.
AIM Workshop "Beyond Kadison-Singer: paving and consequences", December 2014.
AIM Workshop on Classification of Group von Neumann Algebras, January 2018.
Open Problems on Classification of Group von Neumann Algebras (edited by Rolando de Santiago)
AIM Workshop on Set theory and C*-algebras, January 2012.
Open problems on Set theory and C*-algebras (edited by Ilijas Farah, David Kerr, and Martino Lupini)
AIM Workshop on the Cuntz Semigroup, November 2009
A Workshop Report that contains some open questions
Hilbert C*-Modules Homepage, maintained by Michael Frank.
Operator Theory Information Network (OPT-IN), a community hub inspired by OASIS that is aimed at researchers working in operator theory.
Below are lists of books and links to online notes for individuals wishing to learn more about Operator Algebras and related topics. This list is not meant to be comprehensive, but rather to serve as a starting point for studying these topics. Readers should also search on the arXiv and MathSciNet (institutional subscription required) for additional sources.
Notes from a C*-algebra Course at Berkeley by Marc Rieffel (transcribed by Qiaochu Yuan)
A (Very) Short Course on C*-algebras by Dana P. Williams
C*-algebras and Operator Theory by Gerard J. Murphy, 1990
C*-algebras by Example by K. Davidson, 1996
Introduction to Operator Algebras by Li Bing-Ren, 1992
C*-algebras and Their Automorphism Groups by Gert Pedersen, 1979 (updated by Søren Eilers and Dorte Olesen, 2018)
An Invitation to C*-algebras by W. Arveson, 1976
C*-algebras by J. Diximier, 1964
Fundamentals of the Theory of Operator Algebras, Vols. I--IV by R. V. Kadison and J. R. Ringrose, 1997
C*-algebras and W*-algebras by S. Sakai, 1971
Operator Algebras and Quantum Statistical Mechanics, Vols. I and II by Ola Bratteli and Derek William Robinson
Quantum Symmetries on Operator Algebras by David E. Evans and Yasuyuki Kawahigashi
The Symbiosis of C*- and W*-algebras by Nathanial P. Brown
Notes from a von Neumann Algebra Course at Berkeley by Brent Nelson
Notes from a von Neumann Algebra Course at Harvard by Jacob Lurie
Lecture notes from six lectures on von Neumann Algebras by V.S. Sunder
A Gentle Introduction to von Neumann Algebras for Model Theorists by Isaac Goldbring
An Invitation to von Neumann Algebras by V.S. Sunder, 1987
Introduction to Subfactors by Vaughan F.R. Jones and V.S. Sunder, 1997
Lectures on von Neumann algebras by David M. Topping, 1971
Von Neumann Algebras by J. Diximier, 1969
Theory of Operator Algebras Vols. I--III by Masamichi Takesaki, Springer, 1979--2003
Von Neumann Algebras. by Vaughan F.R. Jones, 2015
The Symbiosis of C*- and W*-algebras by Nathanial P. Brown
Operator Algebras: Theory of C*-algebras and von Neumann Algebras by Bruce Blackadar, 2005
Analysis Now by Gert Pedersen, 1989
Functional Analysis: Spectral Theory by V.S. Sunder, 1998
Operators on Hilbert Space by V.S. Sunder, 2016
Lecture Notes on the Spectral Theorem by Dana P. Williams
Lecture Notes on Hilbert Spaces and Quantum Mechanics by N.P. Landsman
Lecture Notes on K-theory by Dana P. Williams
An Introduction to K-Theory for C*-algebras by R. Rørdam, F. Larsen, and N. Laustsen, 2000
K-theory and C*-algebras by N.E. Wegge-Olsen, 1993
K-theory for Operator Algebras by B. Blackadar, 1998
An Introduction to the Classification of Amenable C*-algebras, 2001
The K-book: an introduction to algebraic K-theory by Charles Weibel
Classification of Nuclear, Simple C*-algebras by R. Rørdam, 2001
Introduction to Operator Space Theory by Gilles Pisier, 2003
Completely Bounded Maps and Operator Algebras by Vern Paulsen, 2002
Operator Spaces by Edward G. Effros and Zhong-Jin Ruan, 2000
Morita equivalence and continuous-trace C*-algebras by Iain Rabeurn and Dana P. Williams, 1998
Hilbert C*-modules: A Toolkit for Operator Algebraists by E. Christopher Lance, 1995
Graph Algebras by Iain Raeburn
Graph Algebras: Bridging the Gap Between Analysis and Algebra , edited by Gonzalo Aranda Pino, Francesc Perera Domenech, and Mercedes Siles Molina, 2006
Leavitt Path Algebras by Gene Abrams, Pere Ara, and Mercedes Siles Molina, 2017
Lecture notes on higher-rank graphs and their C*-algebras by Aidan Sims
A Groupoid Approach to C*-algebras by Jean Renault, 1980 Renault's Book
Groupoids, Inverse Semigroups, and their Operator Algebras by Alan L.T. Paterson, 1999
Coordinates in Operator Algebra by Paul Muhly (This is an unfinished monograph from a 1990 CBMS conference. Paul Muhly has graciously made a partially completed version publicly available.)
Hausdorff étale groupoids and their C*-algebras by Aidan Sims
Lecture Notes on C*-algebras by Ian Putnam
A Short Introduction to Graph Groupoids and Their Algebras by Toke Carlsen
Proper Actions and Groupoid Equivalence by Dana P. Williams
Crossed products of C*-algebras by Dana Williams, 2007
Crossed Product C*-algebras and Minimal Dynamics by N. Christopher Phillips
The Peter-Weyl Theorem for Compact Groups by Dana P. Williams
Noncommutative Geometry by Alain Connes, 1995
CBMS conferences (formally, NSF-CBMS Regional Research Conferences) are annual conferences solicited by the Conference Board of the Mathematical Sciences (CBMS) and supported by the National Science Foundation (NSF). CBMS conferences are typically held over five days, and they feature a distinguished speaker delivering ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences. The speaker is strongly encouraged to write up the material of the ten lectures in a CBMS Monograph, which is made available as a co-publication between the CBMS and one of the AMS, SIAM, or IMS.
Below is a list of CBMS conferences related to Operator Algebras. For each we give the location and year of the conference, followed by the monograph and speaker.
University of Puerto Rico, Rio Piedras, 2021
The topic was "K-theory of operator algebras and its applications to geometry and
topology" and the speaker was by Guoliang Yu. The monograph is forthcoming.
University of Wyoming, 2015
From the Basic Homotopy Lemma to the Classification of C*-algebras by Huaxin Lin
University of Louisiana at Lafayette, 2012
The topic was "Topological and Algebraic Regularity Properties of Nuclear C*-Algebras"
and the speaker was Wilhelm Winter, but no monograph was produced.
Texas Christian University, 2009
Topology, C*-Algebras, and String Duality by Jonathan Rosenberg
University of Iowa, 2004
Graph Algebras by Iain Raeburn
University of Colorado, 1995
Index Theory, Coarse Geometry, and Topology of Manifolds by John Roe
University of Oregon, 1993
Classification of Subfactors and Their Endomorphisms by Sorin Popa
Texas Christian University, 1990
The topic was "Coordinates in Operator Algebra: Groupoids & Categories, their
Representations and Applications" and the speaker was Paul Muhly. Paul Muhly never completed
his monograph, but he has graciously made a
partially completed version
available to the public.
United States Naval Academy, 1988
Subfactors and Knots by Vaughan F.R. Jones
Texas Tech University, 1983
Ten Lectures on Operator Algebras by William Arveson
University of Iowa, 1981
Structure of Factors and Automorphism Groups by Masamichi Takesaki
Oakland University, 1979
Dimensions and C*-algebras by Ed Effros
University of Georgia, 1972
Banach Algebra Techniques in the Theory of Toeplitz Operators by Ron G. Douglas
University of Hawaii, 1969
Algebraic and Analytic Aspects of Operator Algebras by Irving Kaplansky