published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

No description available.

No description available.

by Wai-Chiu Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 117-119). / Introduction --- p.1 / Chapter Chapter 1 --- Topological Riesz Spaces --- p.5 / Chapter 1.1 --- Locally convex spaces --- p.5 / Chapter 1.2 --- Ordered vector spaces and Riesz spaces --- p.10 / Chapter 1.3 --- Locally convex Riesz spaces --- p.16 / Chapter 1.4 --- Banach lattices --- p.23 / Chapter Chapter 2 --- Operator Modules and Ideal Cones --- p.32 / Chapter 2.1 --- Operator Modules and Ideal Cones on Banach lattices --- p.32 / Chapter 2.2 --- Half-injective hull and half-surjective hull of operator modules and ideal cones --- p.38 / Chapter 2.3 --- Topologies determined by operator modules and ideal cones --- p.49 / Chapter 2.4 --- Bornologies determined by operator modules and ideal cones --- p.56 / Chapter Chapter 3 --- Banach lattices of operators --- p.63 / Chapter 3.1 --- Cone absolutely summing maps --- p.64 / Chapter 3.2 --- Compact operators on Banach lattices --- p.72 / Chapter 3.3 --- PL-compact operators and locally order precompact operators --- p.85 / Chapter 3.4 --- Almost order bounded sets and semicompact operators --- p.100 / Ref erences --- p.117

Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The purpose of this paper is to present a modified version of Riesz's proof of the spectral theorem for bounded linear operators. The modifications employed are those suggested by S. K. Berberian (5, page 1049). The basic properties of Hilbert space are presented in Chapter I. Chapter II is a discussion of linear operators which includes consideration of functionals, self-adjoint operators, and the spectrum of an operator. The spectral decomposition of a bounded self-adjoint operator is presented in Chapter III. The material in the paper is based primarily on the references in the bibliography. Most of the nontrival proofs have been carried out in detail. / 2031-01-01

Given a function (more generally, a measure) on a locally compact Abelian group, one can define the Toeplitz operators as certain integral transforms of functions on the dual group, where the kernel is the Fourier transform of the original function or measure. In the case of the unit circle, this corresponds to forming a matrix out of the Fourier coefficients in a particular way. We will study the asymptotic eigenvalue distributions of these Toeplitz operators.

Let X be a compact metric space, and Lip(X) is the space of all bounded real-valued Lipschitz functions on X. A linear map T:Lip(X)->Lip(Y) is called disjointness preserving if fg=0 in Lip(X) implies TfTg=0 in Lip(Y). We prove that a biseparating linear bijection T(i.e. T and T^-1 are separating) is a weighted composition operator Tf=hf¡³£p, f is Lipschitz space from X onto R, £p is a homeomorphism from Y onto X, and h(y) is a Lipschitz function in Y.

Motivated by the work of Pólya, Schur, and Turán, a complete characterization of multiplier sequences for the Hermite polynomial basis is given. Laguerre's theorem and a remarkable curve theorem due to Pólya are generalized. Sufficient conditions for the location of zeros in certain strips in the complex plane are determined. Results pertaining to multiplier sequences and complex zero decreasing sequences for other polynomial sets are established. / viii, 178 leaves, bound ; 29 cm. / Thesis (Ph. D.)--University of Hawaii at Manoa, 2007.

Thesis (M.A.)--Wake Forest University. Dept. of Mathematics, 2008. / Vita. Includes bibliographical references (leaves 48-49)