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Now showing items 31-38 of 38

#### K-theory for C*-Algebras and for Topological Spaces

(University of Waterloo, 2015-04-27)

K-theory is the study of a collection of abelian groups that are invariant to C*-algebras or to locally compact Hausdorff spaces. These groups are useful for distinguishing C*-algebras and topological spaces, and they are ...

#### Complexity of Classes of Structures

(University of Waterloo, 2013-08-28)

The main theme of this thesis is studying classes of structures with respect to various measurements of complexity. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on ...

#### Generalized Complex Structures on Kodaira Surfaces

(University of Waterloo, 2014-08-05)

In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-K\"ahler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized ...

#### 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 ...

#### Pick Interpolation and the Distance Formula

(University of Waterloo, 2012-05-09)

The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, ...

#### The Prouhet-Tarry-Escott problem

(University of Waterloo, 2013-01-15)

Given natural numbers n and k, with n>k, the
Prouhet-Tarry-Escott (PTE) problem asks for distinct
subsets of Z, say X={x_1,...,x_n} and
Y={y_1,...,y_n}, such that
x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ...

#### Free semigroup algebras and the structure of an isometric tuple

(University of Waterloo, 2011-06-28)

An n-tuple of operators V=(V_1,…,V_n) acting on a Hilbert space H is said to be isometric if the corresponding row operator is an isometry. A free semigroup algebra is the weakly closed algebra generated by an isometric ...

#### 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 $\alpha-1/2$.