Browsing Pure Mathematics by Title
Now showing items 97-116 of 165
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The O'Nan-Scott Theorem for Finite Primitive Permutation Groups, and Finite Representability
(University of Waterloo, 2009-08-06)The O'Nan-Scott Theorem classifies finite primitive permutation groups into one of five isomorphism classes. This theorem is very useful for answering questions about finite permutation groups since four out of the five ... -
OFF-DIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
(Elsevier, 2020-12-15)Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥A|ran P is said to be an off-diagonal corner of A, and L ... -
On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set
(University of Waterloo, 2007-09-27)We answer to a Wintner's question concerning the sequence of integers composed of primes from a given set. The results generalize and develop the answer to Wintner’s question due to Tijdeman. -
On Amenability Properties and Coideals of Quantum Groups
(University of Waterloo, 2022-07-27)We study amenability type properties of locally compact quantum groups and subobjects of quantum groups realized as submodules of their von Neumann algebras. An important class of such subobjects are the coideals, which ... -
On Asynchronous Interference Channels
(University of Waterloo, 2016-11-15)In the first part of the thesis, a decentralized wireless network of separate transmitter-receiver pairs is studied where there is no central controller to assign the resources to the users and users do not explicitly ... -
On Convolution Squares of Singular Measures
(University of Waterloo, 2010-08-25)We prove that if $1 > \alpha > 1/2$, then there exists a probability measure $\mu$ such that the Hausdorff dimension of its support is $\alpha$ and $\mu*\mu$ is a Lipschitz function of class $\alpha-1/2$. -
On Diagonal Acts of Monoids
(University of Waterloo, 2007-08-30)In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely ... -
On fixed points of self maps of the free ball
(Elsevier, 2018-07-01)In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ... -
On Hopf Ore Extensions and Zariski Cancellation Problems
(University of Waterloo, 2020-04-29)In this thesis, we investigate Ore extensions of Hopf algebras and the Zariski Cancellation problem for noncommutative rings. In particular, we improve upon the existing conditions for when $T=R[x; \sigma, \delta]$ is a ... -
On selfadjoint extensions of semigroups of partial isometries
(American Mathematical Society, 2016)Let S be a semigroup of partial isometries acting on a complex, infinite- dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists ... -
On the Dynamical Wilf-Zeilberger Problem
(University of Waterloo, 2022-08-15)In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by Wilf-Zeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an ... -
On the Erdös-Turán conjecture and related results
(University of Waterloo, 2011-08-29)The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ... -
On the local positivity of line bundles on algebraic surfaces
(University of Waterloo, 2015-01-09)In this thesis, we define a measure for how `positive' an effective line bundle is at a point on a variety, and prove that it is linear on the numerically effective subcone on a smooth, complete, toric surface. -
On the Modular Theory of von Neumann Algebras
(University of Waterloo, 2010-09-17)The purpose of this thesis is to provide an exposition of the \textit{modular theory} of von Neumann algebras. The motivation of the theory is to classify and describe von Neumann algebras which do not admit a trace, and ... -
On the Representation Theory of Semisimple Lie Groups
(University of Waterloo, 2010-08-30)This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ... -
On the Similarity of Operator Algebras to C*-Algebras
(University of Waterloo, 2006)This is an expository thesis which addresses the requirements for an operator algebra to be similar to a <em>C</em>*-algebra. It has been conjectured that this similarity condition is equivalent to either amenability ... -
On the structure of invertible elements in certain Fourier-Stieltjes algebras
(University of Waterloo, 2021-08-27)Let $G$ be a locally compact group. The Fourier-Stieltjes and Fourier algebras, $B(G)$ and $A(G)$ are defined by Eymard to act as dual objects of the measure and group algebras, $M(G)$ and $L^1(G)$, in a sense generalizing ... -
On the Structure of Nonnegative Semigroups of Matrices
(University of Waterloo, 2009-08-18)The results presented here are concerned with questions of decomposability of multiplicative semigroups of matrices with nonnegative entries. Chapter 1 covers some preliminary results which become useful in the remainder ... -
On Transcendence of Irrationals with Non-eventually Periodic b-adic Expansions
(University of Waterloo, 2010-05-18)It is known that almost all numbers are transcendental in the sense of Lebesgue measure. However there is no simple rule to separate transcendental numbers from algebraic numbers. Today research in this direction is about ... -
Operator Spaces and Ideals in Fourier Algebras
(University of Waterloo, 2008-08-11)In this thesis we study ideals in the Fourier algebra, A(G), of a locally compact group G. For a locally compact abelian group G, necessary conditions for a closed ideal in A(G) to be weakly complemented are given, ...