Relevant bibliographies by topics / Hausdorff distance ; Hilbert space ; operator norm

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  1. Journal articles
  2. Dissertations / Theses

Academic literature on the topic 'Hausdorff distance ; Hilbert space ; operator norm'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Hausdorff distance ; Hilbert space ; operator norm"

1

Khoshkam, Mahmood. "Perturbations of type I Aw*-algebras." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 3 (1986): 407–13. http://dx.doi.org/10.1017/s1446788700027579.

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AbstractThe distance between two operator algebras acting on a Hilbert space H is defined to be the Hausdorff distance between their unit balls. We investigate the structural similarities between two close AW*-algebras A and B acting on a Hilbert space H. In particular, we prove that if A is of type I and separable, then A and B are *-isomorphic.
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2

Tripathi, Gyan Prakash, and Nand Lal. "Antinormal composition operators on $ \mbf{\ell^2}$." Tamkang Journal of Mathematics 39, no. 4 (2008): 347–52. http://dx.doi.org/10.5556/j.tkjm.39.2008.9.

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A bounded linear operator $ T $ on a Hilbert space $ H $ is called antinormal if the distance of $ T $ from the set of all normal operators is equal to norm of $ T $. In this paper, we give a complete characterization of antinormal composition operators on $ \ell^2 $, where $ \ell^2 $ is the Hilbert space of all square summable sequences of complex numbers under standard inner product on it.
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3

Atkin, C. J. "The Finsler geometry of groups of isometries of Hilbert Space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 2 (1987): 196–222. http://dx.doi.org/10.1017/s1446788700028202.

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AbstractThe paper deals with six groups: the unitary, orthogonal, symplectic, Fredholm unitary, special Fredholm orthogonal, and Fredholm symplectic groups of an infinite-dimensional Hilbert space. When each is furnished with the invariant Finsler structure induced by the operator-norm on the Lie algebra, it is shown that, between any two points of the group, there exists a geodesic realising this distance (often, indeed, a unique geodesic), except in the full orthogonal group, in which there are pairs of points that cannot be joined by minimising geodesics, and also pairs that cannot even be
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4

Booss-Bavnbek, Bernhelm, Matthias Lesch, and John Phillips. "Unbounded Fredholm Operators and Spectral Flow." Canadian Journal of Mathematics 57, no. 2 (2005): 225–50. http://dx.doi.org/10.4153/cjm-2005-010-1.

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AbstractWe study the gap (= “projection norm” = “graph distance”) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transformand direct methods. In particular, we show the surprising result that this space is connected in contrast to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.
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5

Cooper, Shane, and Anton Savostianov. "Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations." Advances in Nonlinear Analysis 9, no. 1 (2019): 745–87. http://dx.doi.org/10.1515/anona-2020-0024.

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Abstract Homogenisation of global 𝓐ε and exponential 𝓜ε attractors for the damped semi-linear anisotropic wave equation $\begin{array}{} \displaystyle \partial_t ^2u^\varepsilon + y \partial_t u^\varepsilon-\operatorname{div} \left(a\left( \tfrac{x}{\varepsilon} \right)\nabla u^\varepsilon \right)+f(u^\varepsilon)=g, \end{array}$ on a bounded domain Ω ⊂ ℝ3, is performed. Order-sharp estimates between trajectories uε(t) and their homogenised trajectories u0(t) are established. These estimates are given in terms of the operator-norm difference between resolvents of the elliptic operator $\begin{
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6

Chaoba Devi, Yendrembam, Kaushlendra Kumar, Biswajit Chakraborty, and Frederik G. Scholtz. "Revisiting Connes’ finite spectral distance on noncommutative spaces: Moyal plane and fuzzy sphere." International Journal of Geometric Methods in Modern Physics 15, no. 12 (2018): 1850204. http://dx.doi.org/10.1142/s0219887818502043.

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Beginning with a review of the existing literature on the computation of spectral distances on noncommutative spaces like Moyal plane and fuzzy sphere, adaptable to Hilbert–Schmidt operatorial formulation, we carry out a correction, revision and extension of the algorithm provided in [1] i.e. [F. G. Scholtz and B. Chakraborty, J. Phys. A, Math. Theor. 46 (2013) 085204] to compute the finite Connes’ distance between normal states. The revised expression, which we provide here, involves the computation of the infimum of an expression which involves the “transverse” [Formula: see text] component
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7

Burger, Martin, Tapio Helin, and Hanne Kekkonen. "Large noise in variational regularization." Transactions of Mathematics and Its Applications 2, no. 1 (2018). http://dx.doi.org/10.1093/imatrm/tny002.

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Abstract In this paper we consider variational regularization methods for inverse problems with large noise that is in general unbounded in the image space of the forward operator. We introduce a Banach space setting that allows to define a reasonable notion of solutions for more general noise in a larger space provided that one has sufficient mapping properties of the forward operators. A key observation, which guides us through the subsequent analysis, is that such a general noise model can be understood with the same setting as approximate source conditions (while a standard model of bounde
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Dissertations / Theses on the topic "Hausdorff distance ; Hilbert space ; operator norm"

1

Guven, Ayse. "Quantitative perturbation theory for compact operators on a Hilbert space." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23197.

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This thesis makes novel contributions to a problem of practical and theoretical importance, namely how to determine explicitly computable upper bounds for the Hausdorff distance of the spectra of two compact operators on a Hilbert space in terms of the distance of the two operators in operator norm. It turns out that the answer depends crucially on the speed of decay of the sequence of singular values of the two operators. To this end, 'compactness classes', that is, collections of operators the singular values of which decay at a certain speed, are introduced and their functional analytic pro
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