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Robert S. Doran
Robert Stuart Doran (born December 21, 1937) is an American mathematician. He held the John William and Helen Stubbs Potter Professorship in mathematics at Texas Christian University, Texas Christian University (TCU) from 1995 until his retirement in 2016. Doran served as chair of the TCU mathematics department for 21 years. He has also held visiting appointments at the Massachusetts Institute of Technology, the University of Oxford, and the Institute for Advanced Study. He was elected to the board of trustees of the Association of Members of the Institute for Advanced Study, serving as president of the organization for 10 years. He has been an editor for the ''Encyclopedia of Mathematics and its Applications'', Cambridge University Press, a position he has held since 1988. Doran is known for his research-level books, his award-winning teaching, and for his solution to a long-standing open problem due to Irving Kaplansky on a Symmetric algebra, symmetric *-algebra. Personal bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texas Christian University
Texas Christian University (TCU) is a private research university in Fort Worth, Texas. It was established in 1873 by brothers Addison and Randolph Clark as the Add-Ran Male & Female College. It is affiliated with the Christian Church (Disciples of Christ). The campus is located on about 3 miles (5 km) from downtown Fort Worth. TCU is affiliated with, but not governed by, the Disciples of Christ. The university consists of eight constituent colleges and schools and has a classical liberal arts curriculum. It is classified among "R2: Doctoral Universities – High research activity". TCU's mascot is Superfrog, based on the Texas state reptile; the horned frog. For most varsity sports, TCU competes in the Big 12 conference of the NCAA's Division I. As of Fall 2021, the university enrolls around 11,938 students, with 10,222 being undergraduates. History Origins in Fort Worth, 1869–1873 The East Texas brothers Addison and Randolph Clark, with the support of their fathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor's Degree
A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc). In some institutions and educational systems, certain bachelor's degrees can only be taken as graduate or postgraduate educations after a first degree has been completed, although more commonly the successful completion of a bachelor's degree is a prerequisite for further courses such as a master's or a doctorate. In countries with qualifications frameworks, bachelor's degrees are normally one of the major levels in the framework (sometimes two levels where non-honours and honours bachelor's degrees are considered separately). However, some qualifications titled bachelor's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach Algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy \, x \, y\, \ \leq \, x\, \, \, y\, \quad \text x, y \in A. This ensures that the multiplication operation is continuous. A Banach algebra is called ''unital'' if it has an identity element for the multiplication whose norm is 1, and ''commutative'' if its multiplication is commutative. Any Banach algebra A (whether it has an identity element or not) can be embedded isometrically into a unital Banach algebra A_e so as to form a closed ideal of A_e. Often one assumes ''a priori'' that the algebra under consideration is unital: for one can develop much of the theory by considering A_e and then applying the outcome in the ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximate Identity
In mathematics, particularly in functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts as a substitute for an identity element. Definition A right approximate identity in a Banach algebra ''A'' is a net \ such that for every element ''a'' of ''A'', \lim_\lVert ae_\lambda - a \rVert = 0. Similarly, a left approximate identity in a Banach algebra ''A'' is a net \ such that for every element ''a'' of ''A'', \lim_\lVert e_\lambda a - a \rVert = 0. An approximate identity is a net which is both a right approximate identity and a left approximate identity. C*-algebras For C*-algebras, a right (or left) approximate identity consisting of self-adjoint elements is the same as an approximate identity. The net of all positive elements in ''A'' of norm ≤ 1 with its natural order is an approximate identity for any C*-algebra. This is called the canonical approximate identity of a C*-algebra. Appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University
Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the University of Oxford, the oldest university in the English-speaking world; it has buildings in every style of English architecture since late Anglo-Saxon. Oxford's industries include motor manufacturing, education, publishing, information technology and science. History The history of Oxford in England dates back to its original settlement in the Saxon period. Originally of strategic significance due to its controlling location on the upper reaches of the River Thames at its junction with the River Cherwell, the town grew in national importance during the early Norman period, and in the late 12th century became home to the fledgling University of Oxford. The city was besieged during The Anarchy in 1142. The university rose to domina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Upsilon Chi
Beta Upsilon Chi () is the largest Christian social fraternity in the United States. Since its founding at the University of Texas in 1985, ΒΥΧ has spread to twenty-nine campuses. According to the fraternity's official website, Beta Upsilon Chi "exists for the purpose of establishing brotherhood and unity among college men based on the common bond of Jesus Christ." The founding verse of BYX is "Behold how good and how pleasant it is for brothers to dwell together in unity." - Psalm 133:1.About BYX " ''Brothers Under Christ (website).'' Retrieved on July 19, 2010. BYX seeks to set itself apart from other fraternities in its incorporation of cell groups where, separate from weekly fraternity meetings, small groups gather weekly to edify college men through |
Cru (Christian Organization)
Cru (until 2011 known as Campus Crusade for Christ—informally "Campus Crusade" or simply "crusade"—or CCC) is an interdenominational Christian parachurch organization. It was founded in 1951 at the University of California, Los Angeles by Bill Bright and Vonette Zachary Bright. Since then, Cru has expanded its focus to include adult professionals, athletes, and high school students. In 2020, Cru had 19,000 staff members in 190 countries. Campus Crusade for Christ relocated its world headquarters from Arrowhead Springs, San Bernardino, California to Orlando, Florida in 1991. The president of the organization is Steve Sellers. In 2011, Campus Crusade for Christ changed its name to Cru. The name change was intended to avoid association with the word "crusade", which can lead to offense, especially in Muslim countries. A spokesperson for Cru also noted that the organization's work is no longer limited to campuses.. History Early beginnings Campus Crusade for Christ was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Campus Crusade For Christ
Cru (until 2011 known as Campus Crusade for Christ—informally "Campus Crusade" or simply "crusade"—or CCC) is an interdenominational Christian parachurch organization. It was founded in 1951 at the University of California, Los Angeles by Bill Bright and Vonette Zachary Bright. Since then, Cru has expanded its focus to include adult professionals, athletes, and high school students. In 2020, Cru had 19,000 staff members in 190 countries. Campus Crusade for Christ relocated its world headquarters from Arrowhead Springs, San Bernardino, California to Orlando, Florida in 1991. The president of the organization is Steve Sellers. In 2011, Campus Crusade for Christ changed its name to Cru. The name change was intended to avoid association with the word "crusade", which can lead to offense, especially in Muslim countries. A spokesperson for Cru also noted that the organization's work is no longer limited to campuses.. History Early beginnings Campus Crusade for Christ was founde ... [...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, bef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C*-algebras
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 estab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfand–Naimark Theorem
In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra ''A'' is isometrically *-isomorphic to a C*-subalgebra of bounded operators on a Hilbert space. This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C*-algebras since it established the possibility of considering a C*-algebra as an abstract algebraic entity without reference to particular realizations as an operator algebra. Details The Gelfand–Naimark representation π is the direct sum of representations π''f'' of ''A'' where ''f'' ranges over the set of pure states of A and π''f'' is the irreducible representation associated to ''f'' by the GNS construction. Thus the Gelfand–Naimark representation acts on the Hilbert direct sum of the Hilbert spaces ''H''''f'' by : \pi(x) bigoplus_ H_f= \bigoplus_ \pi_f(x)H_f. π(''x'') is a bounded linear operator since it is the direct sum of a family of operators, each one h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
