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Elementary Operators angle of the Son , and the space effect algebra

Author: WangYueQing
Tutor: DuHongKe
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Elementary Operators Norm reachability Projection Idempotent operator Moore-Penrose inverse Subspace angle between the Sequential plot Quantum computing
CLC: O177.1
Type: PhD thesis
Year: 2008
Downloads: 145
Quote: 0
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Abstract


The operator theory is an extremely important area of ??research in functional analysis, since the early 20th century, von Neumann, Hilbert established since the operator theory, operator theory has been the rapid development and penetrate into the mathematics branch to form a group of enduring research topic, the research related to basic mathematics and applied mathematics in many branches, such as algebra, geometry theory, operator perturbation theory, matrix theory, approximation theory, optimization theory, non-commutative probability theory and quantum physics and so on. This article relates to the elementary operator, the angle between the subspace effect algebra is in recent years, active research topic in operator the sub theory and quantum mechanics. These topics, so count the intrinsic relationship of the sub-structure becomes more clear, these studies on operator theory not only has important theoretical significance and application value, a certain sense to enhance the theoretical foundation of the operator theory. This paper studies involving the Elementary Operators in Hilbert space, the three aspects of the angle between the subspace and effect algebra consists of three chapters: the first chapter of the length of n elementary operator norm (norm reachability) and its restrictions on the unitary group norm (norm up). Second, the use of operator block matrix techniques to operator polar decomposition as a tool the operator approximately minimal numerical range of its great value domain and gives a very small value of domain transform Aluthge about the nature of. Define the control operator is given some properties of sub-control operator. Chapter II of the use of space decomposition theory, block operator matrix techniques of the angle between the two subspaces operator norm, spectrum, reduced minimal mode and operator product range closed relationship . Chapter block operator matrix using familiar techniques of quantum computing and generalized quantum gates, the answer to a question raised by Gudder and gives infinite-dimensional extension of some Gudder results. Length of the elementary operator norm (norm up to the research achievements are divided into the following seven areas: (1) a primary constructor) and its restriction to the unitary group norm (Fan reachability) is consistent. (2) the length of n elementary operator norm (norm reachability) and its restrictions on the unitary group norm (norm up) is consistent. (3) defines the minimal value of approximately domain, research about the nature of the domain of a very small value, gives the operator about the relationship between a very small numerical range and its great value domain. Subsequently studied on Aluthgle transform about a very small value domain, gives some of the results. (4) defines the control operator control operator pairs in nature and gives some results. (5) The operator of block matrix techniques, given the fine characterization of the angle between two closed subspaces and the relationship between this angle with the operator norm, spectrum range. (6) studied the sequential plot, the answer to a question posed by Gudder and gives some related results. (7) quantum computing and generalized quantum gates will some of Gudder the results are extended to the infinite-dimensional case.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Hilbert space and linear operator theory
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