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Nuclear operator
About: Nuclear operator is a research topic. Over the lifetime, 2548 publications have been published within this topic receiving 48884 citations.
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Book•
01 Jan 1990TL;DR: In this article, the authors introduce the concept of bounded linear operators on the Bergman space and define a set of operators based on the bounded linear operator on the Hardy space, including the following operators:
Abstract: Bounded linear operators Interpolation of Banach spaces Integral operators on $L^p$ spaces Bergman spaces Bloch and Besov spaces The Berezin transform Toeplitz operators on the Bergman space Hankel operators on the Bergman space Hardy spaces and BMO Hankel operators on the Hardy space Composition operators Bibliography Index.
1,903 citations
Book•
30 Jun 1995TL;DR: In this article, the authors present the fundamental principles of p-summing operators on Hilbert spaces and summing operators in Banach lattices, as well as weakly compact operators on C(K)-spaces with finite cotype.
Abstract: Introduction 1. Unconditioned and absolute summability in Banach spaces 2. Fundamentals of p-summing operators 3. Summing operators on Cp-spaces 4. Operators on Hilbert spaces and summing operators 5. p-Integral operators 6. Trace duality 7. 2-Factorable operators 8. Ultraproducts and local reflexivity 9. p-Factorable operators 10. (q, p)-Summing operators 11. Type and cotype: the basics 12. Randomised series and almost summing operators 13. K-Convexity and B-convexity 14. Spaces with finite cotype 15. Weakly compact operators on C(K)-spaces 16. Type and cotype in Banach lattices 17. Local unconditionality 18. Summing algebras 19. Dvoretzky's theorem and factorization of operators References Indexes.
1,304 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.
1,285 citations
Book•
11 Feb 1972
TL;DR: In this paper, the authors propose a compact operator on Hilbert Space and C*-Algebras, as well as Compact Operators, Fredholm Operators and Index Theory.
Abstract: 1 Banach Spaces.- 2 Banach Algebras.- 3 Geometry of Hilbert Space.- 4 Operators on Hilbert Space and C*-Algebras.- 5 Compact Operators, Fredholm Operators, and Index Theory.- 6 The Hardy Spaces.- 7 Toeplitz Operators.- References.
1,211 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
1,174 citations