The Kadison-Singer problem

Das, Sourav and D, Sukumar (2019) The Kadison-Singer problem. Masters thesis, Indian institute of technology Hyderabad.


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In mathematics, the Kadison-Singer problem, posed in 1959, was a problem in C ∗ - algebra about whether certain extensions of certain linear functionals on certain C ∗ - algebras were unique. The uniqueness was proven in 2013. The statement arose from work on the foundations of quantum mechanics done by Paul Dirac in the 1940s and was formalized in 1959 by Richard Kadison and Isadore Singer. The problem was subsequently shown to be equivalent to numerous open problems in pure mathematics, applied mathematics, engineering and computer science. Kadison, Singer, and most later authors believed the statement to be false, but, in 2013, it was proven true by Adam Marcus, Daniel Spielman and Nikhil Srivastava, who received the 2014 Polya Prize for the achievement. We will discuss about the Kadison-Singer problem for a separable Hilbert space. First of all we will characterize all functions that can possibly have the Kadison-Singer property and then among these which class of functions fail to have the Kadison-Singer property and also finally which class will have the Kadison-Singer property.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Thesis (Masters)
Uncontrolled Keywords: States, Pure State, Unique Extension, MASA
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 17 Jun 2019 10:37
Last Modified: 17 Jun 2019 10:37
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