1,720,966 research outputs found
Limits of hypercyclic operators on Hilbert spaces
Full text linkThis article concerns the operators T E L(H), defined on a separable Hilbert space H, that belong to the norm closure HC(H) in L(H) of the set HC(H) of all hypercyclic operators. Starting from a Herrero's characterization of these operators [11] we deduce some criteria that are very useful in many concrete cases. We also show that if T E L(H) is invertible then T E HC(H) if and only if T-1 E HC(H). This result extends to HC(H) a known result of Kitai and Herrero established for hypercyclic operators, ([13]). (c) 2025 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
On the spectrum of supercyclic/hypercyclic operators
Full text linkThis paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873-875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators T in the case were the dual T & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}T<^>*\end{document} has empty point spectrum
Extensions of hermitian linear functionals
Full text linkWe study, from a quite general point of view, the family of all extensions of a positive hermitian linear functional ω, defined on a dense *-subalgebra A of a topological *-algebra A[ τ] , with the aim of finding extensions that behave regularly. The sole constraint the extensions we are dealing with are required to satisfy is that their domain is a subspace of G(ω) ̄ , the closure of the graph of ω (these are the so-called slight extensions). The main results are two. The first is having characterized those elements of A for which we can find a positive hermitian slight extension of ω, giving the range of the possible values that the extension may assume on these elements; the second one is proving the existence of maximal positive hermitian slight extensions. We show as it is possible to apply these results in several contexts: Riemann integral, Infinite sums, and Dirac Delta
On S-Weyl’s theorem and property (t) for some classes of operators
No full textIn this paper we consider two new variants of the classical
Weyl ’s theorem for operators defined on Banach spaces. These variants
called S-Weyl’s theorem and property (t) are stronger than the more
classical variants of Weyl’s theorem, as a-Weyl’s theorem and property
(ω) studied by several authors. In particular, we explore these two new
variants for operators that commute with an injective quasi-nilpotent
operator
Local Spectral Properties Under Conjugations
Full text linkIn this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and T∈ L(H). We also study the relationship between the quasi-nilpotent part of the adjoint T∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form JT∗J. The theory is exemplified in some concrete cases
Maximal extensions of a linear functional
Full text linkExtensions of a positive hermitian linear functional ω, defined on a dense *-subalgebra A0 of a topological *-algebra A[τ] are analyzed. It turns out that their maximal extensions as linear functionals or hermitian linear functionals are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [2] is revisited from this point of view. Examples mostly taken from the theory of integration are discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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