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Edward George Effros
Edward George Effros (December 10, 1935, Queens, New York City – December 21, 2019, Portland, Oregon) was an American mathematician, specializing in operator algebras and representation theory. His research included " C*-algebras theory and operator algebras, descriptive set theory, Banach space theory, and quantum information." Biography Edward Effros grew up in Great Neck, New York. He finished his undergraduate study in three years at Massachusetts Institute of Technology and received his Ph.D. from Harvard University in 1962. His thesis ''On Representations of C^*-algebras'' was supervised by George Mackey. Effros was a postdoc at Columbia University and then became a faculty member at the University of Pennsylvania. Effros married Rita Brickman in 1967. Their two children, Rachel and Stephen, were born in Philadelphia. In 1980 Edward Effros became a full professor at the University of California at Los Angeles (UCLA), and in 1979 the family relocated to Los Angeles. Rita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queens, New York City
Queens is a borough of New York City, coextensive with Queens County, in the U.S. state of New York. Located on Long Island, it is the largest New York City borough by area. It is bordered by the borough of Brooklyn at the western tip of Long Island to its west, and Nassau County to its east. Queens also shares water borders with the boroughs of Manhattan, the Bronx, and Staten Island (via the Rockaways). With a population of 2,405,464 as of the 2020 census, Queens is the second most populous county in the State of New York, behind Kings County (Brooklyn), and is therefore also the second most populous of the five New York City boroughs. If Queens became a city, it would rank as the fifth most-populous in the U.S. after New York City, Los Angeles, Chicago, and Houston. Approximately 47% of the residents of Queens are foreign-born. Queens is the most linguistically diverse place on Earth and is one of the most ethnically diverse counties in the United States. Queens was es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guggenheim Fellow
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation issues awards in each of two separate competitions: * One open to citizens and permanent residents of the United States and Canada. * The other to citizens and permanent residents of Latin America and the Caribbean. The Latin America and Caribbean competition is currently suspended "while we examine the workings and efficacy of the program. The U.S. and Canadian competition is unaffected by this suspension." The performing arts are excluded, although composers, film directors, and choreographers are eligible. The fellowships are not open to students, only to "advanced professionals in mid-career" such as published authors. The fellows may spend the money as they see fit, as the purpose is to give fellows " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Monetary Fund
The International Monetary Fund (IMF) is a major financial agency of the United Nations, and an international financial institution, headquartered in Washington, D.C., consisting of 190 countries. Its stated mission is "working to foster global monetary cooperation, secure financial stability, facilitate international trade, promote high employment and sustainable economic growth, and reduce poverty around the world." Formed in 1944, started on 27 December 1945, at the Bretton Woods Conference primarily by the ideas of Harry Dexter White and John Maynard Keynes, it came into formal existence in 1945 with 29 member countries and the goal of reconstructing the international monetary system. It now plays a central role in the management of balance of payments difficulties and international financial crises. Countries contribute funds to a pool through a quota system from which countries experiencing balance of payments problems can borrow money. , the fund had XDR 477 billi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Space
In functional analysis, a discipline within mathematics, an operator space is a normed vector space (not necessarily a Banach space) "given together with an isometric embedding into the space ''B(H)'' of all bounded operators on a Hilbert space ''H''.". The appropriate morphisms between operator spaces are completely bounded maps. Equivalent formulations Equivalently, an operator space is a subspace of a C*-algebra. Category of operator spaces The category of operator spaces includes operator systems and operator algebras. For operator systems, in addition to an induced matrix norm of an operator space, one also has an induced matrix order. For operator algebras, there is still the additional ring structure. See also * Gilles Pisier Gilles I. Pisier (born 18 November 1950) is a professor of mathematics at the Pierre and Marie Curie University and a distinguished professor and A.G. and M.E. Owen Chair of Mathematics at the Texas A&M University. He is known for his contributi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Group
In abstract algebra, a partially ordered group is a group (''G'', +) equipped with a partial order "≤" that is ''translation-invariant''; in other words, "≤" has the property that, for all ''a'', ''b'', and ''g'' in ''G'', if ''a'' ≤ ''b'' then ''a'' + ''g'' ≤ ''b'' + ''g'' and ''g'' +'' a'' ≤ ''g'' +'' b''. An element ''x'' of ''G'' is called positive if 0 ≤ ''x''. The set of elements 0 ≤ ''x'' is often denoted with ''G''+, and is called the positive cone of ''G''. By translation invariance, we have ''a'' ≤ ''b'' if and only if 0 ≤ -''a'' + ''b''. So we can reduce the partial order to a monadic property: if and only if For the general group ''G'', the existence of a positive cone specifies an order on ''G''. A group ''G'' is a partially orderable group if and only if there exists a subset ''H'' (which is ''G''+) of ''G'' such that: * 0 ∈ ''H'' * if ''a'' ∈ ''H'' and ''b'' ∈ ''H'' then ''a'' + ''b'' ∈ ''H'' * if ''a'' ∈ ''H'' then -''x'' + ''a'' + ' ... [...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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuclear C*-algebra
In the mathematical field of functional analysis, a nuclear C*-algebra is a C*-algebra A such that the injective and projective C*- cross norms on A \oplus B are the same for every C*-algebra B. This property was first studied by under the name "Property T", which is not related to Kazhdan's property T. Characterizations Nuclearity admits the following equivalent characterizations: * The identity map, as a completely positive map, approximately factors through matrix algebras. By this equivalence, nuclearity can be considered a noncommutative analogue of the existence of partitions of unity. * The enveloping von Neumann algebra is injective. * It is amenable as a Banach algebra. * It is isomorphic to a C*-subalgebra B of the Cuntz algebra \mathcal_2 with the property that there exists a conditional expectation In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Choquet Theory
In mathematics, Choquet theory, named after Gustave Choquet, is an area of functional analysis and convex analysis concerned with measures which have support on the extreme points of a convex set ''C''. Roughly speaking, every vector of ''C'' should appear as a weighted average of extreme points, a concept made more precise by generalizing the notion of weighted average from a convex combination to an integral taken over the set ''E'' of extreme points. Here ''C'' is a subset of a real vector space ''V'', and the main thrust of the theory is to treat the cases where ''V'' is an infinite-dimensional (locally convex Hausdorff) topological vector space along lines similar to the finite-dimensional case. The main concerns of Gustave Choquet were in potential theory. Choquet theory has become a general paradigm, particularly for treating convex cones as determined by their extreme rays, and so for many different notions of ''positivity'' in mathematics. The two ends of a line segmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert Space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term ''Hilbert space'' for the abstract concept that u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Algebra
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, no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Masamichi Takesaki
Masamichi Takesaki (竹崎 正道; born July 18, 1933 in Sendai) is a Japanese mathematician working in the theory of operator algebras. Takesaki studied at Tohoku University, earning a bachelor's degree in 1956, a master's degree in 1958 and a doctorate in 1965. Beginning in 1958 he was a research assistant at the Tokyo Institute of Technology and from 1965 to 1968 he was an associate professor at Tohoku University. From 1968 to 1969 he was a visiting associate professor at the University of Pennsylvania. In 1970, he became a professor at the University of California, Los Angeles. He was also a visiting professor at Aix-Marseille University (1973–74) and Bielefeld University (1975–76). He is known for the Tomita–Takesaki theory, which is about modular automorphisms of von Neumann algebras. This theory was initially developed by Minoru Tomita until 1967, but his work was published only partially (in Japanese) and was quite difficult to understand, drawing little notice, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the '' Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
