Ola Bratteli

Arriving and travelling in Oslo

I am working at the University of Oslo in the mathematics institute , which is located on the seventh floor of Niels Henrik Abels hus . It is building 14 at this map The institute can be reached by taking subway line 3,4,5 or 6 or tram line 10, 17 or 18 to Blindern (Universitetet) . See also all local rail lines and all local bus lines. Here is an Oslo map with search engine. For practical information on how to get from/to the airport to the university or my home, see Oslo Airport information. You may either take the express train Flytoget to Oslo S ( = Jernbanetorget) and there switch to the metro T-banen to Majorstua (for my home) or to Blindern (for the university). Or you may take the bus Flybussekspressen at the stop B15 just outside the terminal building towards Majorstua and jump off at the next last stop Marienlyst (200 meters from my home) or third last stop Vestre Aker Kirke (500 meters from the university). More and updated information about local transport in Oslo can be found (in Norwegian) at Trafikanten. Here is a map of the 2 km walk from Gyldenløve Hotel to the Mathematics Institute. (From Bogstadveien 20 to Moltke Moes vei 35) (R 168 = Bogstadveien, R 161 = Kirkeveien; you may use the obvious diagonal shortcut Tusentrippen over the fields from Suhms gate).

Research interests

My research interests has been and are in various subjects related to operator algebras: Approximately finite dimensional C*-algebras, specific models in quantum statistical mechanics and quantum field theory, unbounded derivations on operator algebras, equilibrium states in quantum statistical mechanics, C*-dynamical systems, one-parameter semigroups on Banach spaces and their generators, dissipations on operator algebras, locality and differential operators, noncommutative vector fields on operator algebras, actions of Lie algebras on operator algebras, parabolic differential equations on Lie groups, classification of real rank zero C*-algebras, real rank zero algebras obtained as inductive limits and their classification, representations of Cuntz algebras related to wavelet theory.

Scientific papers

• For early papers, see the Curriculum Vitae or MathSciNet (Mathematical Reviews). For recent papers, see the list below or Los Alamos Archives.

• O.Bratteli, A.Kishimoto and D.W.Robinson, Approximately inner derivations., Mathematica Scandinavica 103.1 (2008),141-160
• O.Bratteli, A.Kishimoto and D.W.Robinson, Rohlin flows on the Cuntz algebra $O_\infty$, J.Functional Analysis 248 (2007), 472-511
• O.Bratteli and A.Kishimoto, AF flows and continuous symmetries, Reviews of Mathematical Physics 13 (2001), 1505-1528
• O.Bratteli and P.E.T.Jorgensen, Wavelet filters and infinite-dimensional unitary groups, in Proceedings of the International Conference on Wavelet Analysis and Applications, Donggao Deng, Daren Huang, Rong-Qing Jia, Wei Lin, Jianzhong Wang (eds.), American Mathematical Society/International Press (2002), pp. 35--64.
• O.Bratteli, P.E.T.Jorgensen, K.H.Kim and F.Roush, Decidability of the isomorphism problem for stationary AF-algebras. This paper is published in two parts as follows:
• Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups, Ergod.Theory and Dyn.Sys. 21 (2001), 1625-1655 with Corrigendum, Ergod.Theory and Dyn.Sys. 22 (2002), 633.
• Computation of isomorphism invariants for stationary dimension groups, Ergod.Theory and Dyn.Sys. 22 (2002), 99 - 127.
• O.Bratteli, P.E.T.Jorgensen and V.Ostrovskyi, Representation theory and numerical AF-invariants: The representations and centralizers of certain states on O_d, Mem. Amer. Math. Soc. 168 (2004), no. 797, 178 pp. (expected publication date is February 28, 2004). Updated pdf file.
• O.Bratteli and P.E.T.Jorgensen, Convergence of the cascade algorithm at irregular scaling functions, in D. Larson and L. Baggett, eds., "The Functional and Harmonic Analysis of Wavelets and Frames", Contemp. Math. 247 (1999), 93--130.
• O.Bratteli and A.Kishimoto, Homogeneity of the pure state space of the Cuntz algebra, J. Functional Analysis 171(2000), 331-345.
• O. Bratteli and A.Kishimoto, Trace scaling automorphisms of certain stable AF algebras II, Quarterly J. Math. 51(2000) 131-154.
• O.Bratteli, P.E.T.Jorgensen, K. Hang Kim and F. Roush, Non-stationarity of isomorphism between AF algebra defined by stationary Bratteli diagrams, Ergodic Theory and Dynamical Systems 20 (2000),1639-1656.
• O.Bratteli, D.E.Evans and P.E.T.Jorgensen, Compactly Supported Wavelets and Representations of the Cuntz Relations, in amputated form (without pictures) in Applied and Computational Harmonic Analysis 8(2000), 166-196.
• O.Bratteli, P.E.T.Jorgensen, A.Kishimoto and R.F.Werner, Pure states on O_d, J. Operator Theory 43 (2000), 97-143.
• O.Bratteli, G.A.Elliott, D.E.Evans and A.Kishimoto, Homotopy of a pair of approximately commuting unitaries in a simple C*-algebra, J. Functional Analysis 160(1998), 466 - 523.
• O.Bratteli, P.E.T.Jorgensen and D.W.Robinson, Spectral asymptotics of periodic elliptic operators, Math.Zeitschrift. 232 (1999) 4, 621-650
• O.Bratteli and P.E.T.Jorgensen, A connection between multiresolution wavelet theory of scale N and representations of the Cuntz algebra O_N, in S.Doplicher et al., eds., Operator Algebras and Quantum Field Theory, International Press (1997), 151-163.
• O.Bratteli and P.E.T.Jorgensen, Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N, Integr.equ.oper.theory 28(1997) 382-443.
• O.Bratteli and P.E.T.Jorgensen, Iterated function systems and permutation representations of the Cuntz algebra, Memoirs of AMS 663(1999) 1-89.
• O.Bratteli, A.Kishimoto and D.W.Robinson, Abundance of invariant and almost invariant pure states of C*-dynamical systems, Comm.Math.Phys.187(1997) 491-507.
• O.Bratteli, P.E.T.Jorgensen and G.Price, Endomorphisms of B(H), in Arveson et al.,Quantization, Nonlinear Partial Differential Equations, and Operator Algebra, Proc.Symp.Pure Math. 59, AMS (1996) 93-138)

Curriculum vitae

Mathematical relatives

My mathematical genealogy (pupil - Ph.D. adviser relations) is: Ola Bratteli (Oslo, b.1946) - Erling Størmer (Oslo, b.1937) - Richard V. Kadison (Pennsylvania, b.1926) - Marshall Harvey Stone (Harvard, 1903 -1989)- George David Birkhoff (Harvard, 1884 -1944) - Eliakim Hastings Moore (Chicago, 1862 - 1932) - Hubert Anson Newton (Yale, 1830-1896) - Michel Chasles ( Ecole Polytechnique,1793 - 1880) - Simeon Denis Poisson (Ecole Polytechnique, 1781 - 1840) - Joseph Louis Lagrange (Berlin, Academie des Sciences,1736 - 1813) - Leonhard Euler (Basel - St.Petersburg, 1707 - 1783) - Johann Bernoulli (Basel, 1667 - 1748) - Jacob Bernoulli (Basel, 1654 - 1705) - Gottfried Wilhelm von Leibniz (Hannover, 1646 - 1716) - Erhard Weigel (Ph.D. in Leipzig 1650)

Source: The mathematics genealogy project. One of the connections appears precarious: Hubert Anson Newton is described as a selfmade professor who never produced a doctoral thesis. On the other hand: "Poisson's only other student was Michel Chasles (1814), who went to Yale where he advised only H.A. (Hubert Anson) Newton (1850)" A more probable scenario is described in an article by Karen Hunger Parshall in Annals of Science 41 (1984), 313-333: "When Newton was appointed to the professorship in mathematics in 1855, he was immediately granted a year's leave of absence so that he could better prepare himself for the job. He spent his year in Paris listening to Michel Chasles's (1793-1880) lectures on geometry at the Sorbonne. These lectures left a permanent impression on Newton even though the majority of his subsequent work focused on astronomical problems. In fact, this undying interest manifested itself almost thiry years later in the geometrical topic which Newton and Moore worked out for the latter's dissertation research. In urging Moore to study in Europe, Newton most likely wanted to assure his student of an equally lasting and rewarding experience." More details in the footnote on p.315 in op.cit., and even more in Steve Battersons article "The Father of the Father of American Mathematics, Notices of the AMS 55 (2008), 352-363.

My Erdös number is 3 by the connection:

Ola Bratteli - Ki Hang Kim and Fred W. Roush - Jozsef Denes - Paul Erdös

Connections of order 4 to Erdös

Ola Bratteli - Derek Robinson - Elliott Lieb - Dan Kleitman - Paul Erdös

Ola Bratteli - George Elliott - David Handelman - Denis Higgs - Paul Erdös

My coauthor Palle E.T.Jorgensen has Erdös number 3 by by the same connection as me. Several others of my coauthors have Erdös number 3 by different connections: Bruce Blackadar, Trond Digernes, Uffe Haagerup, Richard H. Herman, Alex Kumjian, Mikael Rørdam, Erling Størmer.

Source: The Erdös Number project.

Compute your own Erdös number here.

Scientific impact

According to ISI web of science Ola Bratteli has been cited in 2720 scientific papers to date . Allegedly this is the highest number of citing papers in the period 1940 - 28 October 2010 for the scientific work of any Norwegian mathematician (The common misspellings Bratelli, Brattelli and the less common Brateli and Blatteli of my last name are taken into account). I am indebted to Leiv Storesletten for pointing this out. (Please shoot me a mail if this information is wrong)

Picking out the 2463 papers where my name is spelled correctly (to 16 March 2010), the subject matter of 1166 is mathematics, 809 is mathematical physics, 410 is multidiciplinary physics and 251 is applied mathematics.

By far the most cited original paper by Ola Bratteli is item 1 in the CV which is the paper where AF algebras were introduced. It has been cited in 283 papers to mid 2007. The next papers in this ranking is the first paper on unbouded derivations on C*-algebras (5, 64 citations), the paper of reduction of real rank in inductive limits (80, 45 citations) and the paper 24 on crossed products by product type actions with 36 citations.

But these numbers are completely dwarfed by the number of citations of the two volumes in the research monograph on operator algebras and quantum statistical mechanics with Derek Robinson: The various editions of Volume 1 have been cited in 899 papers and Volume 2 have been cited in 710 papers. The last two numbers are difficult to compare with the earlier numbers since many papers cite both volumes of Bratteli-Robinson and then they are only counted once in the overall count. However, another search for papers citing volume 1 or/and volume 2 of Bratteli-Robinson gives 1366 papers. Thus 656 papers cite Volume 1 only, 467 papers cite Volume 2 only, while 243 papers cite both (ajour by mid 2007)

Another thing which is clear from the ISI web list is that the papers which are cited much are papers which open doors to new problems and research directions, while papers which solves "deep" problems and thus close doors often are consigned to silence. I guess this is a common experience.

The MR author citation index gives numbers which are quite different from those above since it counts citations and citing authors rather than citing papers, and thus it counts several citations of the same author in the same paper with multiplicity. Also the MR index restricts to citations in pure mathematics journals after 1997-2000. To date (28 October 2010) the MR index mentions 1300 citations by 788 authors.

Note also that the numbers from ISI were obtained by using the cited reference search in ISI. If one starts using a general author search instead and then use the citation report device, the number of citations to Ola Bratteli becomes much smaller. The reason is that the book with Derek Robinson is not indexed within Web of Science, but articles in Web of Science which refer to the book are included in the count of citations obtained by cited reference search.

A critical evaluation of the use of citation indices may be found here.

"Typically, AF is characterized as a storm of electrical energy that travels in spinning wavelets across both atria, causing these upper chambers to quiver or to fibrillate at 300 to 600 times per minute. "