|
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] |
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. Most familiar as the name of the property that says something like 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 years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman emper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Los Angeles Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2011 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 * Deaths by year {{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 Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * January 26 – A 10-year German–Polish declaration of non-aggression is signed by Nazi Germany and the Second Polish Republic. * January 30 ** In Nazi Germany, the political power of federal states such as Prussia is substantially abolished, by the "Law on the Reconstruction of the Reich" (''Gesetz über den Neuaufbau des Reiches''). ** Franklin D. Roosevelt, President of the United States, signs the Gold Reserve Act: all gold held in the Federal Reserve is to be surrendered to the United States Department of the Treasury; immediately following, the President raises the statutory gold price from US$20.67 per ounce to $35. * February 6 – F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product System
Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * 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 product * Cup product ... [...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 alge ... [...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''. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as 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 frequencies of the harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on R''n'' is still an area of ongoing research, particularly concerning Fourier transformation on more general objects such as tempered di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_-_09.JPG "Click for more on -> University Of California, Los Angeles Alumni")
.png "Click for more on -> Harmonic Analysis")