Products of orthogonal projections as Carleman operators
type: Item
instance of: scholarly article
title: Products of orthogonal projections as Carleman operators
zbMATH Open document ID: 0935.47002
DOI: 10.1007/BF01225529
author: Manuela Nees
published in: Integral Equations and Operator Theory
publication date: 2000-04-10T00:00:00Z
review text: Let \(X\neq\emptyset\) and let \(\mu\) be a \(\sigma\)-finite measure on \(X\) such that the Hilbert space \(L^2(X,\mu)\) is infinite-dimensional and separable. Let \(H\) be an infinite-dimensional separable Hilbert space. An operator \(A: H\to L_q(X,\mu)\) is said to be a Carleman operator if there is a measurable function \(k: X\to H\) such that (ii) \(D(A)\subseteq \{f\in H:\langle f,k(\cdot)\rangle_H\in L_q(X,\mu)\}\) and (ii) \(Af= \langle f,k(\cdot)\rangle_H\) for all \(f\in D(A)\). Let \(Q\), \(P\) be two orthogonal projections on \(H\). Then \(QP\) is either a Carleman operator or a semi-Fredholm operator with finite defect.
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 1346933
zbMATH Keywords: finite defect
zbMATH Keywords: angle between two subspaces
zbMATH Keywords: Carleman operator
zbMATH Keywords: orthogonal projections
zbMATH Keywords: semi-Fredholm operator
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1346933