本文關(guān)鍵詞：Dirichlet級數(shù)空間上的復(fù)合算子　出處：《武漢大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Dirichlet 級數(shù) 復(fù)合算子 再生核 不變子空間 拓?fù)浣Y(jié)構(gòu)

【摘要】：本文主要研究Dirichlet級數(shù)空間上的(加權(quán))復(fù)合算子的一些基本性質(zhì),其中包括不變子空間,循環(huán)性和拓?fù)浣Y(jié)構(gòu)等.此外,我們也考慮多變量再生核函數(shù)空間上的復(fù)對稱加權(quán)復(fù)合算子.第一章,主要介紹了幾種解析函數(shù)空間上復(fù)合算子理論的研究背景和研究現(xiàn)狀.即介紹了Dirichlet級數(shù)構(gòu)成的解析函數(shù)空間以及多變量再生核函數(shù)空間的相關(guān)概念及其上的復(fù)合算子.第二章,研究了系數(shù)平方可和的Dirichlet級數(shù)構(gòu)成的Hilbert空間H上復(fù)合算子的不變子空間問題.特別地,我們證明了由某些復(fù)合算子生成的強(qiáng)閉單位算子代數(shù)是自反的,并給出了一個非代數(shù)復(fù)合算子的判據(jù).第三章,研究了Hilbert空間H上的加權(quán)復(fù)合算子.本章刻畫了加權(quán)復(fù)合算子的Hermitian性,Fredholm性和可逆性,并且給出了緊和可逆加權(quán)復(fù)合算子的譜.第四章,研究了Dirichlet級數(shù)空間H∞上的復(fù)合算子空間C(H∞)的拓?fù)浣Y(jié)構(gòu).出乎意料的是,我們證明了c(H∞)中存在兩個緊算子但不在同一個連通分支中.這與單變量或多變量的經(jīng)典空間H∞上的情形(其上所有緊復(fù)合算子都在同一個連通分支中)形成了鮮明對比.第五章,研究了全純Dirichlet級數(shù)空間H(E,βs)上復(fù)合算子的一些性質(zhì).這些性質(zhì)包括Fredholm性,Hilbert-Schmidt性,譜和循環(huán)性.此外,本章還給出了有關(guān)復(fù)合算子范數(shù)的一個公式,這個公式回答了Cowen-MacCluer提出的一個問題.第六章,研究了多變量再生核函數(shù)空間Hs(s0)上加權(quán)復(fù)合算子的復(fù)對稱性.我們首先給出了Hs上關(guān)于某個特殊共軛算子的復(fù)對稱加權(quán)復(fù)合算子的具體形式；接著,完全刻畫了此類算子的緊性,Hilbert-Schmidt性,正規(guī)性和等距性,并且給出了它們的譜半徑估計.
[Abstract]:In this paper, we mainly study some basic properties of (weighted) composition operator on Dirichlet series space, including invariant subspace, circularity and topological structure, etc. We also consider the complex symmetric weighted composition operators on the space of multivariable reproducing kernel functions. Chapter 1. This paper mainly introduces the research background and present situation of composition operator theory on several analytic function spaces, that is, the correlation between analytic function spaces composed of Dirichlet series and multivariable reproducing kernel function spaces. Concept and composition operators on it. Chapter 2. In this paper, we study the invariant subspace problem of composition operator on Hilbert space H, which is composed of Dirichlet series with squared summable coefficients. We prove that the strongly closed unit operator algebras generated by some composition operators are reflexive and give a criterion for nonalgebraic composition operators. Chapter 3. The weighted composition operators on Hilbert space H are studied. In this chapter, the Hermitian property and reversibility of weighted composition operators are characterized. And the spectrum of compact and reversible weighted composition operators is given. In chapter 4th, the topological structure of composition operator space C _ H _ 鈭，

本文編號：1359716