|
Ola Bratteli
Ola Bratteli (24 October 1946 – 8 February 2015) was a Norwegian mathematician. He was a son of Trygve Bratteli and Randi Bratteli (née Larssen). He received a PhD degree in 1974. He was appointed as professor at the University of Trondheim in 1980 and at the University of Oslo in 1991. He was a member of the Norwegian Academy of Science and Letters. Selected works *with Derek W. Robinson: ''Operator Algebras and Quantum Statistical Mechanics'' (Springer-Verlag, 2 volumes, 1980) *''Derivations, Dissipations and Group Actions on C*-algebras'' (Springer-Verlag, 1986) *with Palle T. Jørgensen: ''Wavelets through a looking glass, the world of the spectrum'' (Birkhäuser, 2002) See also *Approximately finite-dimensional C*-algebra *Bratteli diagram *Bratteli–Vershik diagram In mathematics, a Bratteli–Veršik diagram is an ordered, essentially simple Bratteli diagram (''V'', ''E'') with a homeomorphism on the set of all infinite paths called the Veršhik transformati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norwegian Mathematicians
A mathematician is a scholar in the fields of mathematics. They solve and research mathematical problems which can be applied in real life or completely abstract (pure). This article covers notable mathematicans from Norway. A pioneer of modern mathematics, Niels Henrik Abel contributed greatly towards various fields of mathematics during his short life. He died in 1829, aged 26, from tuberculosis. German mathematician Felix Klein spoke of his reluctance "to part from this ideal type of researcher". In 2001, the Abel Prize was established in his honour. Other notable mathematicians include (in alphabetical order) Carl Anton Bjerknes, Vilhelm Bjerknes, Bernt Michael Holmboe, who is known for being Abel's teacher and tutor, Sophus Lie, Idun Reiten, Atle Selberg, Thoralf Skolem and Carl Størmer. Alphabetical order ''"Aa" appears under "å" as they are considered different representations of the same letter.'' See also *Archiv for Mathematik og Naturvidenskab *Bjerknes (lunar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oslo
Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of in 2019, and the metropolitan area had an estimated population of in 2021. During the Viking Age the area was part of Viken. Oslo was founded as a city at the end of the Viking Age in 1040 under the name Ánslo, and established as a ''kaupstad'' or trading place in 1048 by Harald Hardrada. The city was elevated to a bishopric in 1070 and a capital under Haakon V of Norway around 1300. Personal unions with Denmark from 1397 to 1523 and again from 1536 to 1814 reduced its influence. After being destroyed by a fire in 1624, during the reign of King Christian IV, a new city was built closer to Akershus Fortress and named Christiania in honour of the king. It became a municipality ('' formannskapsdistrikt'') on 1 January 1838. The city fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bratteli–Vershik Diagram
In mathematics, a Bratteli–Veršik diagram is an ordered, essentially simple Bratteli diagram (''V'', ''E'') with a homeomorphism on the set of all infinite paths called the Veršhik transformation. It is named after Ola Bratteli and Anatoly Vershik. Definition Let ''X'' = be the set of all paths in the essentially simple Bratteli diagram (''V'', ''E''). Let ''E''min be the set of all minimal edges in ''E'', similarly let ''E''max be the set of all maximal edges. Let ''y'' be the unique infinite path in ''E''max. (Diagrams which possess a unique infinite path are called "essentially simple".) The Veršhik transformation is a homeomorphism φ : ''X'' → ''X'' defined such that φ(''x'') is the unique minimal path if ''x'' = ''y''. Otherwise ''x'' = (''e''1, ''e''2,...) , ''e''''i'' ∈ ''E''''i'' where at least one ''e''''i'' ∉ ''E''max. Let ''k'' be the smallest such integer. Then φ(''x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The University Of Oslo
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulation, dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The Norwegian University Of Science And Technology
An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, '' Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2015 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day The following pages, corresponding to the Gregorian calendar, list the historical events, births, deaths, and holidays and observances of the specified day of the year: Footnotes See also * Leap year * List of calendars * List of non-standard ... * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1946 Births
Events January * January 6 - The 1946 North Vietnamese parliamentary election, first general election ever in Vietnam is held. * January 7 – The Allies recognize the Austrian republic with its 1937 borders, and divide the country into four Allied-occupied Austria, occupation zones. * January 10 ** The first meeting of the United Nations is held, at Methodist Central Hall Westminster in London. ** ''Project Diana'' bounces radar waves off the Moon, measuring the exact distance between the Earth and the Moon, and proves that communication is possible between Earth and outer space, effectively opening the Space Age. * January 11 - Enver Hoxha declares the People's Republic of Albania, with himself as prime minister of Albania, prime minister. * January 16 – Charles de Gaulle resigns as head of the Provisional Government of the French Republic, French provisional government. * January 17 - The United Nations Security Council holds its first session, at Church House, Westmin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Prydz (biochemist)
Hans Prydz (4 March 1868 – 19 August 1957) was a Norwegian physician and politician for the Conservative Party. Personal life He was born in Grini in Bærum, as the son of lieutenant colonel Christen Edvard Prydz (1835–1909) and his wife Isakine Wilhelmine Caspara Abel (1840–1924). He was a great-grandson of Peter Blankenborg Prydz and Søren Georg Abel, both former politicians.Hans Prydz — Norwegian Social Science Data Services (NSD) His mother was a niece of the mathematician Niels Henrik Abel. He married Inger Sandberg in October 1893. They had two daughters and one son. Their oldest daughter married a Nicolai Ditlev Ammon Ræder, a relative of the poli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Per Brandtzæg
Per Brandtzæg (9 June 1936 – 11 September 2016) was a Norwegian dentist. He was a professor of medicine at the University of Oslo. In November 2006 he was proclaimed Commander of the Order of St. Olav in recognition of his work. He was a member of the Norwegian Academy of Science and Letters The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick Unive .... He was also known to the general public as a proponent to retry the case of Fredrik Fasting Torgersen. References 1936 births 2016 deaths Norwegian dentists Academic staff of the University of Oslo Members of the Norwegian Academy of Science and Letters {{Norway-academic-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bratteli Diagram
In mathematics, a Bratteli diagram is a combinatorial structure: a Graph (discrete mathematics), graph composed of vertices labelled by positive integers ("level") and unoriented edges between vertices having levels differing by one. The notion was introduced by Ola Bratteli in 1972 in the theory of operator algebras to describe directed sequences of finite-dimensional algebras: it played an important role in Elliott's classification of approximately finite-dimensional C*-algebra, AF-algebras and the theory of subfactors. Subsequently Anatoly Vershik associated dynamical systems with infinite paths in such graphs. Definition A Bratteli diagram is given by the following objects: * A sequence of sets ''V''''n'' ('the vertices at level ''n'' ') labeled by positive integer set N. In some literature each element v of ''V''''n'' is accompanied by a positive integer ''b''''v'' > 0. * A sequence of sets ''E''''n'' ('the edges from level ''n'' to ''n'' + 1 ') ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trygve Bratteli
(11 January 1910 – 20 November 1984) was a Norwegian newspaper editor and politician with the Norwegian Labour Party. He served as the 26th prime minister of Norway from 1971 to 1972 and again from 1973 to 1976. He was president of the Nordic Council in 1978. Background Bratteli was born on the island of Nøtterøy at Færder in Vestfold, Norway. His parents were Terje Hansen Bratteli (1879–1967) and Martha Barmen (1881–1937). He attended school locally, having many jobs including: work in fishing, as a coal miner and on a building site. Over a 9- to 10-month period, Bratteli travelled with whalers to Antarctica, where he worked in a guano factory at South Georgia Island. He was a student at the socialist school at Malmøya in 1933. Oscar Torp, chairman of the Norwegian Labour Party, asked him to become editor of ''Folkets Frihet'' in Kirkenes and later editor of '' Arbeiderungdommen'' which was published by the Socialist Youth League of Norway. For a period durin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximately Finite-dimensional C*-algebra
In mathematics, an approximately finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality was first defined and described combinatorially by Ola Bratteli. Later, George A. Elliott gave a complete classification of AF algebras using the ''K''0 functor whose range consists of ordered abelian groups with sufficiently nice order structure. The classification theorem for AF-algebras serves as a prototype for classification results for larger classes of separable simple amenable stably finite C*-algebras. Its proof divides into two parts. The invariant here is ''K''0 with its natural order structure; this is a functor. First, one proves ''existence'': a homomorphism between invariants must lift to a *-homomorphism of algebras. Second, one shows ''uniqueness'': the lift must be unique up to approximate unitary equivalence. Classification then follows from what is known as ''the inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
