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Lawrence G. Brown
Lawrence G. Brown (born February 6, 1943 in St. Louis, Missouri) is an American mathematician who studies operator algebras. Brown studied at Harvard University, graduating in 1968 with George Mackey as his advisor and thesis entitled ''On the Structure of Locally Compact Groups''. He was a professor at Purdue University until his retirement. With Peter A. Fillmore and Ronald G. Douglas, he developed the Brown-Douglas-Fillmore theory in the theory of operator algebras based on techniques of algebraic topology. See also * Real rank (C*-algebras) * Brown measure External links Lawrence G. Brown's homepage at PurdueHis page at the Mathematics Genealogy Project References * Brown, L. G.; Douglas, R. G.; Fillmore, P. A., "Extensions of C*-algebras and K-homology", ''Annals of Mathematics'' (2) 105 (1977), no. 2, 265–324. 20th-century American mathematicians 21st-century American mathematicians 1943 births Living people Operator theorists Harvard University alumni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...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 n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From St
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Alumni
The list of Harvard University people includes notable graduates, professors, and administrators affiliated with Harvard University. For a list of notable non-graduates of Harvard, see notable non-graduate alumni of Harvard. For a list of Harvard's presidents, see President of Harvard University. Eight President of the United States, Presidents of the United States have graduated from Harvard University: John Adams, John Quincy Adams, Rutherford B. Hayes, John F. Kennedy, Franklin Delano Roosevelt, Theodore Roosevelt, George W. Bush, and Barack Obama. Bush graduated from Harvard Business School, Hayes and Obama from Harvard Law School, and the others from Harvard College. Over 150 Nobel Prize winners have been associated with the university as alumni, researchers or faculty. Nobel laureates Pulitzer Prize winners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Theorists
Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another space, e.g.: ** Linear operator ** Differential operator ** Integral operator (other) Computers * Computer operator, an occupation * Operator (computer programming), a type of computer program function * Operator (extension), an extension for the Firefox web browser, for reading microformats * Ableton Operator, a software synthesizer developed by Ableton Science * Operator (biology), a segment of DNA regulating the activity of genes * Operator (linguistics), a special category including wh- interrogatives * Operator (physics), mathematical operators in quantum physics Music * Operator (band), an American hard rock band * Operators, a synth pop band led by Dan Boeckner * ''Operator'' (album), a 2016 album by Mstrkrft * "Oper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1943 Births
Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: The Soviet Union announces that 22 German divisions have been encircled at Stalingrad, with 175,000 killed and 137,650 captured. * January 4 – WWII: Greek-Polish athlete and saboteur Jerzy Iwanow-Szajnowicz is executed by the Germans at Kaisariani. * January 11 ** The United States and United Kingdom revise previously unequal treaty relationships with the Republic of China (1912–1949), Republic of China. ** Italian-American anarchist Carlo Tresca is assassinated in New York City. * January 13 – Anti-Nazi protests in Sofia result in 200 arrests and 36 executions. * January 14 – January 24, 24 – WWII: Casablanca Conference: Franklin D. Roosevelt, President of the United States; Winston Churchill, Prime Minister of the United Kingdom; and Generals Charles de Gaulle and Henri Giraud of the Free French forces meet secretly at the Anfa Hotel in Casablanca, Morocco, to plan the ... [...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 empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brown Measure
In mathematics, the Brown measure of an operator in a finite factor is a probability measure on the complex plane which may be viewed as an analog of the spectral counting measure (based on algebraic multiplicity) of matrices. It is named after Lawrence G. Brown. Definition Let \mathcal be a finite factor with the canonical normalized trace \tau and let I be the identity operator. For every operator A \in \mathcal, the function \lambda \mapsto \tau(\log \left, A-\lambda I\), \; \lambda \in \Complex, is a subharmonic function and its Laplacian in the distributional sense is a probability measure on \Complex \mu_A(\mathrm(a+b\mathbb)) := \frac\nabla^2 \tau(\log \left, A-(a+b\mathbb) I\)\mathrma\mathrmb which is called the Brown measure of A. Here the Laplace operator \nabla^2 is complex. The subharmonic function can also be written in terms of the Fuglede−Kadison determinant In mathematics, the Fuglede−Kadison determinant of an invertible operator in a finite factor is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Algebra
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of operator algebras are phrased in algebraic terms, while the techniques used are highly analytic.''Theory of Operator Algebras I'' By Masamichi Takesaki, Springer 2012, p vi Although the study of operator algebras is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Overview Operator algebras can be used to study arbitrary sets of operators with little algebraic relation ''simultaneously''. From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator. In general operator algebras are non-commutative rings. An operator alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Rank (C*-algebras)
In mathematics, the real rank of a C*-algebra is a noncommutative analogue of Lebesgue covering dimension. The notion was first introduced by Lawrence G. Brown and Gert K. Pedersen. Definition The real rank of a unital C*-algebra ''A'' is the smallest non-negative integer ''n'', denoted RR(''A''), such that for every (''n'' + 1)-tuple (''x''0, ''x''1, ... ,''x''''n'') of self-adjoint elements of ''A'' and every ''ε'' > 0, there exists an (''n'' + 1)-tuple (''y''0, ''y''1, ... ,''y''''n'') of self-adjoint elements of ''A'' such that \sum_^n y_i^2 is invertible and \lVert \sum_^n (x_i - y_i)^2 \rVert < \varepsilon. If no such integer exists, then the real rank of ''A'' is infinite. The real rank of a non-unital C*-algebra is defined to be the real rank of its unitalization. Comparisons with dimension If ''X'' is a[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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