Closed embeddings of Hilbert spaces
type: Item
instance of: scholarly article
title: Closed embeddings of Hilbert spaces
zbMATH Open document ID: 1198.46022
author: Petru A. Cojuhari
author: Aurelian Gheondea
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-07T00:00:00Z
full work available at URL: http://hdl.handle.net/11693/22231
review text: The authors extend the notion of continuous embedding of Hilbert spaces to that of closed embedding in such a way that unbounded kernel operators are allowed, and investigate its connection with operator ranges, its properties and especially uniqueness properties. They exemplify certain constructions by pointing out closed embeddings that appear when comparing some Hilbert spaces of holomorphic functions on the disk (Hardy, Dirichlet, Bergman). They prove the closed embedding for certain homogeneous Sobolev spaces on the semi-axis and the Euclidean space \(\mathbb{R}^n\) into the ambient \(L_2\) space and obtain an equivalent characterization of absolutely continuous bounded kernel operators in terms of closed embeddings, see \textit{P.\,A.\thinspace Cojuhari} and \textit{A.\,Gheondea} [J.~Math.\ Anal.\ Appl.\ 304, No.\,2, 584--598 (2005; Zbl 1092.46004)]. The authors show that closed embedding is a special representation of a Hilbert space induced by a positive selfadjoint operator within the ambient Hilbert space.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 46C05
Mathematics Subject Classification ID: 46C07
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 5731664
zbMATH Keywords: Hilbert space
zbMATH Keywords: continuous embedding
zbMATH Keywords: operator range
zbMATH Keywords: closed embedding
zbMATH Keywords: kernel operator
zbMATH Keywords: homogeneous Sobolev space
zbMATH Keywords: absolute continuity
MaRDI profile type: Publication
OpenAlex ID: W2095998626
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DOI: 10.1016/J.JMAA.2010.02.027
description: scientific article; zbMATH DE number 5731664