|
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 contributions to several fields of mathematics, including functional analysis, probability theory, harmonic analysis, and operator theory. He has also made fundamental contributions to the theory of C*-algebras. Gilles is the younger brother of French actress Marie-France Pisier. Research Pisier has obtained many fundamental results in various parts of mathematical analysis. Geometry of Banach spaces In the "local theory of Banach spaces", Pisier and Bernard Maurey developed the theory of Rademacher type, following its use in probability theory by J. Hoffman–Jorgensen and in the characterization of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier proved that super-reflexive Banach spaces can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nouméa
Nouméa () is the capital and largest city of the French special collectivity of New Caledonia and is also the largest francophone city in Oceania. It is situated on a peninsula in the south of New Caledonia's main island, Grande Terre, and is home to the majority of the island's European, Polynesian ( Wallisians, Futunians, Tahitians), Indonesian, and Vietnamese populations, as well as many Melanesians, Ni-Vanuatu and Kanaks who work in one of the South Pacific's most industrialised cities. The city lies on a protected deepwater harbour that serves as the chief port for New Caledonia. At the September 2019 census, there were 182,341 inhabitants in the metropolitan area of Greater Nouméa (), 94,285 of whom lived in the city (commune) of Nouméa proper. 67.2% of the population of New Caledonia live in Greater Nouméa, which covers the communes of Nouméa, Le Mont-Dore, Dumbéa and Païta. History The first European to establish a settlement in the vicinity was British ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rademacher Type
In functional analysis, the class of ''B''-convex spaces is a class of Banach space. The concept of ''B''-convexity was defined and used to characterize Banach spaces that have the strong law of large numbers by Anatole Beck in 1962; accordingly, "B-convexity" is understood as an abbreviation of Beck convexity. Beck proved the following theorem: A Banach space is ''B''-convex if and only if every sequence of independent, symmetric, uniformly bounded and Radon random variables in that space satisfies the strong law of large numbers. Let ''X'' be a Banach space with norm , , , , . ''X'' is said to be ''B''-convex if for some ''ε'' > 0 and some natural number ''n'', it holds true that whenever ''x''1, ..., ''x''''n'' are elements of the closed unit ball of ''X'', there is a choice of signs ''α''1, ..., ''α''''n'' ∈ such that :\left\, \sum_^ \alpha_ x_ \right\, \leq (1 - \varepsilon) n. Later authors have shown that B-convexity is equivalent to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marius Junge
Marius may refer to: People *Gaius Marius (157 BC-86 BC), Roman statesman, seven times consul. Arts and entertainment * ''Marius'' (play), a 1929 play by Marcel Pagnol * "Marius" (short story), a 1957 story by Poul Anderson * ''Marius'' (1931 film), a French adaptation of Pagnol's play, directed by Alexander Korda * ''Marius'' (2013 film), a French adaptation of Pagnol's play, directed by Daniel Auteuil Places * Marius (Laconia), a town of ancient Laconia, Greece * Măriuș, a village in Valea Vinului, Satu Mare County, Romania * Marius (crater), on the Moon * Marius Hills, on the Moon Other uses * Marius (name), a male given name, a Roman clan name and family name, and a modern name or surname * Marius (commando), Alain Alivon (born 1965), French Navy officer * Marius (giraffe), a giraffe euthanized at the Copenhagen Zoo in 2014 See also * * * Mario (other) * Maria (other) * Mary (other) Mary may refer to: People * Mary (name), a feminin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C*-algebra
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous linear operators on a complex Hilbert space with two additional properties: * ''A'' is a topologically closed set in the norm topology of operators. * ''A'' is closed under the operation of taking adjoints of operators. Another important class of non-Hilbert C*-algebras includes the algebra C_0(X) of complex-valued continuous functions on ''X'' that vanish at infinity, where ''X'' is a locally compact Hausdorff space. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establi ... [...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] |
Nigel Kalton
Nigel John Kalton (June 20, 1946 – August 31, 2010) was a British-American mathematician, known for his contributions to functional analysis. Career Kalton was born in Bromley and educated at Dulwich College, where he excelled at both mathematics and chess. After studying mathematics at Trinity College, Cambridge, he received his PhD, which was awarded the Rayleigh Prize for research excellence, from Cambridge University in 1970. He then held positions at Lehigh University in Pennsylvania, Warwick, Swansea, University of Illinois, and Michigan State University, before becoming full professor at the University of Missouri, Columbia, in 1979. He received the Stefan Banach Medal from the Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society o ... in 2005. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fréchet Space
In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces are Fréchet spaces. Spaces of infinitely differentiable functions are typical examples of Fréchet spaces, many of which are typically Banach spaces. A Fréchet space X is defined to be a locally convex metrizable topological vector space (TVS) that is complete as a TVS, meaning that every Cauchy sequence in X converges to some point in X (see footnote for more details).Here "Cauchy" means Cauchy with respect to the canonical uniformity that every TVS possess. That is, a sequence x_ = \left(x_m\right)_^ in a TVS X is Cauchy if and only if for all neighborhoods U of the origin in X, x_m - x_n \in U whenever m and n are sufficiently large. Note that this definition of a Cau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joram Lindenstrauss
Joram Lindenstrauss ( he, יורם לינדנשטראוס) (October 28, 1936 – April 29, 2012) was an Israeli mathematician working in functional analysis. He was a professor of mathematics at the Einstein Institute of Mathematics. Biography Joram Lindenstrauss was born in Tel Aviv. He was the only child of a pair of lawyers who immigrated to Israel from Berlin. He began to study mathematics at the Hebrew University of Jerusalem in 1954 while serving in the army. He became a full-time student in 1956 and received his master's degree in 1959. In 1962 Lindenstrauss earned his Ph.D. from the Hebrew University (dissertation: ''Extension of Compact Operators'', advisors: Aryeh Dvoretzky, Branko Grünbaum). He worked as a postdoc at Yale University and the University of Washington in Seattle from 1962 - 1965. He was appointed senior lecturer at the Hebrew University in 1965, associate professor on 1967 and full professor in 1969. He became the Leon H. and Ada G. Miller Memorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Per Enflo
Per H. Enflo (; born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved problems that had been considered fundamental. Three of these problems had been open for more than forty years: * The basis problem and the approximation problem and later * the invariant subspace problem for Banach spaces. In solving these problems, Enflo developed new techniques which were then used by other researchers in functional analysis and operator theory for years. Some of Enflo's research has been important also in other mathematical fields, such as number theory, and in computer science, especially computer algebra and approximation algorithms. Enflo works at Kent State University, where he holds the title of University Professor. Enflo has earlier held positions at the Miller Institute for Basic Research in Science at the University of California, Berkeley, Stanford University, École Polytechnique, (Paris) and The Royal Institute of Techn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Journal Of Mathematics
'' Israel Journal of Mathematics'' is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem (Magnes Press). Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section F), the journal publishes articles on all areas of mathematics. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.70, and its 2009 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... was 0.754. External links * Mathematics journals Publications established in 1963 English-language journals Bimonthly journals Hebrew University of Jerusalem {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Convexity
In mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity was first introduced by James A. Clarkson in 1936. Definition A uniformly convex space is a normed vector space such that, for every 00 such that for any two vectors with \, x\, = 1 and \, y\, = 1, the condition :\, x-y\, \geq\varepsilon implies that: :\left\, \frac\right\, \leq 1-\delta. Intuitively, the center of a line segment inside the unit ball must lie deep inside the unit ball unless the segment is short. Properties * The unit sphere can be replaced with the closed unit ball in the definition. Namely, a normed vector space X is uniformly convex if and only if for every 00 so that, for any two vectors x and y in the closed unit ball (i.e. \, x\, \le 1 and \, y\, \le 1 ) with \, x-y\, \ge \varepsilon , one has \left\, \right\, \le 1-\delta (note that, given \varepsilon , the corresponding value of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulus Of Convexity
In mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ''ε''-''δ'' definition of uniform convexity as the modulus of continuity does to the ''ε''-''δ'' definition of continuity. Definitions The modulus of convexity of a Banach space (''X'', , , ·, , ) is the function defined by :\delta (\varepsilon) = \inf \left\, where ''S'' denotes the unit sphere of (''X'', , , , , ). In the definition of ''δ''(''ε''), one can as well take the infimum over all vectors ''x'', ''y'' in ''X'' such that and . The characteristic of convexity of the space (''X'', , , , , ) is the number ''ε''0 defined by :\varepsilon_ = \sup \. These notions are implicit in the general study of uniform convexity by J. A. Clarkson (; this is the same paper containing the statements of Clarkson ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
