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William Arveson
William B. Arveson (22 November 1934 – 15 November 2011) was a mathematician specializing in operator algebras who worked as a professor of Mathematics at the University of California, Berkeley. Biography Arveson obtained his Ph.D. from UCLA in 1964 with thesis advisor Henry Dye and thesis ''Prediction theory and group representations''. Of particular note is Arveson's work on completely positive maps. One of his earlier results in this area is an extension theorem for completely positive maps with values in the algebra of all bounded operators on a Hilbert space. This theorem led naturally to the question of injectivity of von-Neumann algebras in general, which culminated in work by Alain Connes relating injectivity to hyperfiniteness. One of the major features of Arveson's work was the use of algebras of operators to elucidate single operator theory. In a series of papers in the 1960s and 1970s, Arveson introduced noncommutative analogues of several concepts from classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncommutative
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as noncommutative operations. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many centuries implicitly assumed. Thus, this property was not named until the 19th century, when new algebraic structures started to be studied. Definition A binary operation * on a set ''S'' is ''commutative'' if x * y = y * x for all x,y \in S. An operation that is not commutative is said to be ''noncommutative''. One s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men ( Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Los Angeles Alumni
A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Universities typically offer both undergraduate education, undergraduate and postgraduate education, postgraduate programs. The first universities in Europe were established by Catholic Church, Catholic monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law and notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2011 Deaths
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked below. 2025 2024 2023 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 1986 Earlier years ''Deaths in years earlier than this can usually be found in the main articles of the years.'' See also * Lists of deaths by day * Deaths by year (category) {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1934 Births
Events January–February * January 1 – The International Telecommunication Union, a specialist agency of the League of Nations, is established. * January 15 – The 8.0 1934 Nepal–Bihar earthquake, Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity scale, Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * February 6 – 6 February 1934 crisis, French political crisis: The French far-right leagues rally in front of the Palais Bourbon, in an attempted coup d'état against the French Third Republic, Third Republic. * February 9 ** Gaston Doumergue forms a new government in France. ** Second Hellenic Republic, Greece, Kingdom of Romania, Romania, Turkey and Kingdom of Yugoslavia, Yugoslavia form the Balkan Pact. * February 12–February 15, 15 – Austrian Civil War: The Fatherland Front (Austria), Fatherland Front consolidates its power in a series of clashes across the country. * February 16 – The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product System
Product may refer to: Business * Product (business), an item that can be offered to a market to satisfy the desire or need of a customer. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Product (mathematics) Algebra * Direct product Set theory * Cartesian product of sets Group theory * Direct product of groups * Semidirect product * Product of group subsets * Wreath product * Free product * Zappa–Szép product (or knit product), a generalization of the direct and semidirect products Ring theory * Product of rings * Ideal operations, for product of ideals Linear algebra * Scalar multiplication * Matrix multiplication * Inner product, on an inner product space * Exterior product or wedge product * Multiplication of vectors: ** Dot product ** Cross product ** Seven-dimensional cross product ** Triple product, in vector calculus * Tensor product Topology * Product topology Algebraic topology * Cap prod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Algebras
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. Two basic examples of von Neumann algebras are as follows: *The ring L^\infty(\mathbb R) of essentially bounded measurable functions on the real line is a commutative von Neumann algebra, whose elements act as multiplication operators by pointwise multiplication on the Hilbert space L^2(\mathbb R) of square-integrable functions. *The algebra \mathcal B(\mathcal H) of all bounded operators on a Hilbert space \mathcal H is a von Neumann algebra, n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis, spectral analysis, and neuroscience. The term "harmonics" originated from the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are integer multiples of one another, as are the freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
