Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 54 for “"Banach space"”.
-
Floquet Theory on Banach Space
<p>In this thesis we study Floquet theory on a Banach space. We are concerned about the linear differential equation of the form: <em>y'</em>(<em>t</em>) = <em>A</em>(<em>t</em>)<em>y</em>(<em>t</em>), where t ∈ R, <em>y</em>(<em>t</em>) is a function with values in a Banach space <em>X</em>, and …
-
Integration and Differentiation in a Banach Space
… the Integral to functions that have values in a Banach space. The differentiation of functions that are not of bounded variation and the extension of the Denjoy integral to vector-valued functions are studied in detail. It is shown that a BVG$\sb\*$ function that has a measurable scalar …
-
On Some Classical Banach Space Concepts in Operator Space Theory
… that the nth-dimensional operator Hilbert space OHn is a subspace of an operator space which is completely isomorphic to a completely complemented subspace of a non-commutative Lp space over a QWEP separable type III factor. Using this, we proved that the completely p-summing norm of the …
-
Lyapunov Exponents and Invariant Manifold for Random Dynamical Systems in a Banach Space
… exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this theorem to establish …
-
Finite Metric Subsets of Banach Spaces
… introduction of a new isometric invariant of a Banach space. This is Property AI-I. A Banach space has Property AI-I if whenever a finite metric space almost-isometrically embeds into the space, it isometrically embeds. To study this property we introduce two further properties that can be …
-
Nearly Representable Operators (dunford-Pettis, Radon-Nikodym)
… of nearly represent- able operators from a Banach space X to a Banach space Y. These are the operators that map X-valued uniformly bounded martingales that are Cauchy in the Pettis norm into Y-valued martingales that converge almost everywhere.
-
Discontinuous homomorphisms from Banach algebras of operators
The relationship between a Banach space X and its Banach algebra of bounded operators B(X) is rich and complex; this is especially so for non-classical Banach spaces. In this thesis we consider questions of the following form: does there exist a Banach space X such that B(X) has a particular …
-
Nonstandard theory of vector measures
… techniques from nonstandard theories of measure spaces and Banach spaces are brought together to develop a nonstandard theory of Banach space valued measures. In particular, constructions of countably additive vector measures from internal vector measures are presented. An integration theory of …
-
A study of stochastic processes in Banach spaces
The theory of 2-convex norms is applied to Banach space valued random vectors. Use is made of a norm on random vectors, introduced by Pisier, equal to the 2-absolutely summing norm on an associated space of operators. For Q the variance of some centred Gaussian random vector in a separable Banach …
-
Hermite-Hadamard inequality in the geometry of banach spaces
… inequalities in studying the geometry of a Banach space. Motivated by the Hermite-Hadamard inequality, a new family of norms is defined, which is called the p-HH-norm. The research outcomes of this thesis make significant contributions in Banach space theory, the theory of means and the …
-
Properties and Legacies of Tsirelson Space
Tsirelson space is a reflexive, separable Banach space constructed by Boris Tsirelson to be the first example of a Banach space that does not contain an isomorphic copy of the sequence spaces c_0 or l_p for 1\leqslant p<infinity. We begin with the construction of the classical sequence spaces c_0 …
-
Nonstandard vector integrals and vector measures
… simple functions from an internal measure space to the nonstandard extension of a Banach space. We take suitable equivalence classes and identify the subspace of S-integrable functions with a space of functions from a Loeb space into the nonstandard hull of a Banach space. This space …
-
Spaces of Compact Operators
In this dissertation we study the structure of spaces of operators, especially the space of all compact operators between two Banach spaces X and Y. Work by Kalton, Emmanuele, Bator and Lewis on the space of compact and weakly compact operators motivates much of this paper. Let L(X,Y) be the Banach …
-
Banach Spaces on Topological Ramsey Structures
<p>A Banach space <em>T<sub>1</sub>(d, θ)</em> with a Tsirelson-type norm is constructed on the top of the topological Ramsey space <em>T<sub>1</sub></em> defined by Dobrinen and Todorcevic [6]. Finite approximations of the isomorphic subtrees are utilised in constructing the norm. The subspace on …
-
Dunford-Pettis operators on L(,1) and the complete continuity property
… of bounded linear operators from $L\sb1$ into a Banach space ${\cal X}$ and the internal geometry of ${\cal X}$ has long been evident. The Radon-Nikodym property (RNP) and strong regularity arose as operator theoretic properties but were later realized as geometric properties.
-
Norm-determining subspaces
… thesis will centre on the concept of norming subspaces in the dual of a Banach space. We shall consider a weakly-dense subspace V of E', and the natural norm it generates on E. If this new norm is equivalent to the original norm on E, then V is called norming or norm-determining.
-
LOCALIZATION TECHNIQUES FOR RENORMING
… in order to improve the norm of a normed space X. This means to make the geometrical and topological properties of the unit ball of the given normed space as close as possible to those of the unit ball of a Hilbert space. In this work we study different types of geometrical properties. In …
-
Geometrical and Martingale characterizations of UMD and Hilbert spaces
Suppose that X is a real or complex Banach space with norm $\vert \cdot \vert$. Then X is a Hilbert space if and only if $E\vert x + Y\vert \geq 1$ for all x $\in$ X and all X-valued Bochner integrable functions Y on the Lebesgue unit interval satisfying EY = 0 and $\vert Y\vert \geq$ 1 a.e. This …
Page 1 of 3