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Hilbert C*-modules are mathematical objects that generalise the notion of a Hilbert space, in that they endow a linear space with an "inner product" that takes values in a C*-algebra. Hilbert C*-modules were first introduced in the work of Irving Kaplansky in 1953, which developed the theory for commutative, unital algebras. In the 1970s the theory was extended to non-commutative C*-algebras independently by William Lindall Paschke and Marc Rieffel, the latter in a paper that used Hilbert C*-modules to construct a theory of induced representations of C*-algebras. Hilbert C*-modules are crucial to Kasparov's formulation of KK-theory, and provide the right framework to extend the notion of Morita equivalence to C*-algebras. They can be viewed as the generalization of vector bundles to noncommutative C*-algebras and as such play an important role in noncommutative geometry, notably in C*-algebraic quantum group theory, and groupoid C*-algebras.
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In functional analysis, a discipline within mathematics, an operator space is a normed vector 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.
In physics, quantum dynamics is the quantum version of classical dynamics. Quantum dynamics deals with the motions, and energy and momentum exchanges of systems whose behavior is governed by the laws of quantum mechanics. Quantum dynamics is relevant for burgeoning fields, such as quantum computing and atomic optics.
Gilles I. Pisier 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.
Kalyan Bidhan Sinha is an Indian mathematician. He is a professor at the Jawaharlal Nehru Centre for Advanced Scientific Research, and Professor Emeritus for life of the Indian Statistical Institute.
Mohammad Sal Moslehian. is an Iranian mathematician and a professor of mathematics at Ferdowsi University of Mashhad, Iran. He is the President of the Iranian Mathematical Society for the period of 2021-2024 and an invited member of the Iranian Academy of Sciences. His Erdős number is 3. He is known for his contribution to the operator and norm inequality. He has developed the orthogonality in Hilbert C*-modules and has significant contributions to operator means. He established noncommutative versions of martingale and maximum inequalities that play an essential role in noncommutative probability spaces. In addition, he has written several expository papers discussing research and education, as well as promoting mathematics.
References
- ↑ "Vern Paulsen". uh.edu. Retrieved May 10, 2017.
- ↑ "Vern Paulsen". uwaterloo.ca. 2 July 2015. Retrieved May 10, 2017.
- ↑ "Vern Paulsen - IQC People". Institute for Quantum Computing. Retrieved 2019-03-15.
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