Topic
Operator norm
About: Operator norm is a research topic. Over the lifetime, 5702 publications have been published within this topic receiving 120300 citations. The topic is also known as: bounded linear operator.
Papers published on a yearly basis
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Papers
TL;DR: Dunford and Schwartz as discussed by the authors provided a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis, and emphasized the significance of the relationships between the abstract theory and its applications.
Abstract: This classic text, written by two notable mathematicians, constitutes a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis. Dunford and Schwartz emphasize the significance of the relationships between the abstract theory and its applications. This text has been written for the student as well as for the mathematician—treatment is relatively self-contained. This is a paperback edition of the original work, unabridged, in three volumes.
3,545 citations
Book•
1 Jan 1995TL;DR: In this paper, the authors provide global and asymptotic estimates for the eigenvalues of - + q when q is real and for -+ q when 1 is complete.
Abstract: Linear operations in Banach spaces Entropy numbers, s-numbers, and eigenvalues Unbounded linear operators Sesquilinear forms in Hilbert spaces Sobolev spaces Generalized Dirichlet and Neumann boundary-value problems Second-order differential operators on arbitrary open sets Capacity and compactness criteria Essential spectra Essential spectra of general second-order differential operators Global and asymptotic estimates for the eigen-values of - + q when q is real. Estimates for the singular values of - + q when 1 is complete Bibliography Notation index Subject index
1,986 citations
TL;DR: In this article, a necessary and sufficient condition for linear transformations in L(A1, A2) to preserve trace of Hermitian and positive semidefinite operators is presented.
1,787 citations
Book•
14 Jul 2009TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
Abstract: The evolution of the state of many systems modeled by linear partial difierentialequations (PDEs) or linear delay-difierential equations can be described by operatorsemigroups. The state of such a system is an element in an inflnite-dimensionalnormed space, whence the name \inflnite-dimensional linear system".The study of operator semigroups is a mature area of functional analysis, which isstill very active. The study of observation and control operators for such semigroupsis relatively more recent. These operators are needed to model the interactionof a system with the surrounding world via outputs or inputs. The main topicsof interest about observation and control operators are admissibility, observability,controllability, stabilizability and detectability. Observation and control operatorsare an essential ingredient of well-posed linear systems (or more generally systemnodes). Inthisbookwedealonlywithadmissibility, observabilityandcontrollability.We deal only with operator semigroups acting on Hilbert spaces.This book is meant to be an elementary introduction into the topics mentionedabove. By \elementary" we mean that we assume no prior knowledge of flnite-dimensional control theory, and no prior knowledge of operator semigroups or ofunbounded operators. We introduce everything needed from these areas. We doassume that the reader has a basic understanding of bounded operators on Hilbertspaces, difierential equations, Fourier and Laplace transforms, distributions andSobolev spaces on
1,553 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 16 |
| 2023 | 59 |
| 2022 | 103 |
| 2021 | 109 |
| 2020 | 107 |