by Yu Man-hei. / Bibliography: leaves 80-81 / Thesis (M.Phil.)--Chinese University of Hong Kong, 1982

Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 29.

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We study the geometric classification of Banach spaces via Lipschitz, uniformly continuous, and coarse mappings. We prove that a Banach space which is uniformly homeomorphic to a linear quotient of lp is itself a linear quotient of lp when p<2. We show that a Banach space which is Lipschitz universal for all separable metric spaces cannot be asymptotically uniformly convex. Next we consider coarse embedding maps as defined by Gromov, and show that lp cannot coarsely embed into a Hilbert space when p> 2. We then build upon the method of this proof to show that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it is isomorphic to a subspace of L0(??) for some probability space (Ω,B,??).

A natural problem that arises in the study of derivations on a Banach algebra is to classify the commutators in the algebra. The problem as stated is too broad and we will only consider the algebra of operators acting on a given Banach space X. In particular, we will focus our attention to the spaces $\lambda I and $\linf$. The main results are that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact and the operators on $\linf$ which are commutators are those not of the form $\lambda I + S$ with $\lambda\neq 0$ and $S$ strictly singular. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17, 1513 - 1534) to obtain these results and use this generalization to obtain partial results about the commutators on spaces $\mathcal{X}$ which can be represented as $\displaystyle \mathcal{X}\simeq \left ( \bigoplus_{i=0}^{\infty} \mathcal{X}\right)_{p}$ for some $1\leq p\leq\infty$ or $p=0$. In particular, it is shown that every non - $E$ operator on $L_1$ is a commutator. A characterization of the commutators on $\ell_{p_1}\oplus\ell_{p_2}\oplus\cdots\oplus\ell_{p_n}$ is also given.

In this paper, we introduce a new class of general-ized co-complementarity problems in Banach spaces. An iterative algorithm for finding approximate solutions of these problems is considered. Some convergence results for this iterative algorithm are derived and several existence results are obtained.

We study the geometric classi&#64257;cation of Banach spaces via Lipschitz, uniformly continuous, and coarse mappings. We prove that a Banach space which is uniformly homeomorphic to a linear quotient of lp is itself a linear quotient of lp when p<2. We show that a Banach space which is Lipschitz universal for all separable metric spaces cannot be asymptotically uniformly convex. Next we consider coarse embedding maps as de&#64257;ned by Gromov, and show that lp cannot coarsely embed into a Hilbert space when p> 2. We then build upon the method of this proof to show that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it is isomorphic to a subspace of L0(??) for some probability space (&#937;,B,??).

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 49-50).

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 20, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Nigel J. Kalton. Vita. Includes bibliographical references.

The purpose of this paper is two fold. Firstly, to introduce and study the Silov Boundary of a Banach algebra of continuous complex valued functions defined on a compact Hausdorff space X. Secondly, to apply the definition of Silov Boundary to more general families of functions, namely, to linear spaces and semi-groups of functions. It will be seen that in these latter cases, existence of the Silov Boundary depends on certain restricting assumptions about the linear space or semi-group. [...]