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Showing 1 to 11 of 11 for “"Normed Space"”.
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Unbounded linear operators in seminormed spaces
… theory is usually studied in the setting of normed or Banach spaces. However, careful examination of proofs shows that in many cases the Hausdorff property of normed spaces is not used. Even in those cases where explicit use of the Hausdorff property is made, one can often get around this …
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Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators
… corresponding operators on a partially ordered normed space. We extend results which are well-known for M-matrices to this more general setting. We investigate two different notions of an M-operator, where we focus on two questions: 1. For which types of partially ordered normed spaces do the …
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Stochastic Stefan problems: existence, uniqueness, and modeling of market limit orders
… equations of this kind. We also derive the space and time regularities of the solutions and the associated boundaries via Kolmogorov's Continuity Theorem in a defined normed space. Moreover, we model the evolution of market limit orders in completely continuous settings using such equations, …
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Generalized DF spaces
A DF space is a topological vector space sharing certain essential properties with the strong duals of Frechet spaces. The class of DF spaces includes not only all such duals, but also every· normed space and many other spaces besides. The definition of a DF space is due to Grothendieck, who …
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Metric Geometry of Finite Subset Spaces
<p>If X is a (topological) space, the nth finite subset space of X, denoted by X(n), consists of n-point subsets of X (i.e., nonempty subsets of cardinality at most n) with the quotient topology induced by the unordering map q:X^n--> X(n), (x_1,...,x_n)-->{x_1,...,x_n}. That is, a subset A of X(n) …
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LOCALIZATION TECHNIQUES FOR RENORMING
… isomorphisms 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 …
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Applications of the fourier transform to convex geometry
… problem in hyperbolic and spherical spaces, and the lower dimensional Busemann-Petty problem in the hyperbolic space. In the Euclidean space we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions. In chapter five we …
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Lipschitz Geometry of Banach and Metric Spaces
… and Hölder continuous maps between a Banach space X and its dual space X^*, the space of continuous linear functionals. The existence of these maps is related to the smoothness of the norm of the space and isomorphic invariants called type and cotype will play a central role as well. The main …
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Topics in high-dimensional geometry and optimal transport
… of well-complemented almost Euclidean subspaces of spaces uniformly isomorphic to $\ell_2^n$. First, we show that there exist constants $\alpha,\epsilon>0$ such that for every positive integer $n$ there is a continuous odd function $\psi : S^m\to S^n$, with $m\geq \alpha n$, such that the …
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Reflexivity, elementary operators and cohomology
<p>Let H be a separable complex Hilbert space and let B(H) be the set of all bounded operators on H. In this dissertation, we show that if S is a n-dimensional subspace of B( H), then S is [ 2n ]-reflexive, where [t] denotes the largest integer that is less than or equal to t.</p><p>We obtain some …
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Contributions to Lattice-like Properties on Ordered Normed Spaces
Banachverbände spielen sowohl in der Theorie als auch in der Anwendung von geordneten normierten Räume eine bedeutende Rolle. Einerseits erweisen sich viele in der Praxis relevanten Räume als Banachverbände, andererseits ermöglichen die Vektorverbandsstruktur und die enge Beziehung zwischen Ordnung …