On a class of operators on Hilbert space with applications to factorization and systems theory
type: Item
instance of: scholarly article
title: On a class of operators on Hilbert space with applications to factorization and systems theory
zbMATH Open document ID: 0618.93012
DOI: 10.1016/0022-247X(84)90228-2
author: Alan Schumitzky
author: M. H. Milman
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: A class of operators is defined in a Hilbert resolution space setting that offers a new perspective on problems of causal invertibility, special factorization, and the theory of quadratic cost optimization problems for dynamical systems. The major results include an extension of the special factorization to a class of noncompact operators and the definition of an abstract state space. These results are then used to obtain an optimal feedback solution to an abstract linear regular- quadratic cost problem.
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 4003989
zbMATH Keywords: Hilbert resolution space
zbMATH Keywords: causal invertibility
zbMATH Keywords: factorization
zbMATH Keywords: quadratic cost optimization problems for dynamical systems
zbMATH Keywords: noncompact operators
zbMATH Keywords: abstract state space
zbMATH Keywords: optimal feedback solution
zbMATH Keywords: abstract linear regular- quadratic cost problem
MaRDI profile type: Publication
cites work: Q5590313
cites work: Resolution space, operators and systems
cites work: Basic optimal estimation and control problems in Hilbert space
cites work: On the generalization of the Volterra principle of inversion
cites work: A solution to a problem of J. R. Ringrose
cites work: Factorization and quadratic cost problems in Hilbert spaces
cites work: State in Hilbert Space
cites work: Q3950367
cites work: Q4742620
cites work: A basic optimization problem in linear systems
Recommended article: On a factorization of operators on finite dimensional Hilbert spaces
Recommended article: Factorization theorems and the structure of operators on Hilbert space
Recommended article: Q3811232
Recommended article: The module factorization of operators on Hilbert space
Recommended article: Hilbert space factorization and Fourier type of operators
Recommended article: Factorization of operators. Theory and applications
Recommended article: Factoring operators over Hilbert-Schmidt maps and vector measures
Recommended article: On a class of Hilbert-Schmidt operators
Recommended article: Factorization of operator functions in a Hilbert space
Recommended article: Factorization of Hilbert operators
description: scientific article; zbMATH DE number 4003989