On a class on nondensely defined contractions and their extensions
type: Item
instance of: scholarly article
title: On a class on nondensely defined contractions and their extensions
zbMATH Open document ID: 0956.47002
DOI: 10.1007/BF02366101
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-03-28T00:00:00Z
review text: Let \(H\) be a complex Hilbert space, \(\alpha\in (0,\pi/2]\) and \(I\) the identity operator in \(H\). If a linear operator \(A: D(A)\subset H\to H\) satisfies \(\|\sin\alpha A\pm i\cos\alpha I\|\leq 1\), then, in case \(D(A)= H\), we say that \(A\) belongs to the class \(C(\alpha)\) and in the case \(D(A)\neq H\) the operator \(A\) is a \(C(\alpha)\)-suboperator. The paper deals with the following general problem: if \(A\) is a \(C(\alpha)\)-suboperator with \(\alpha\in [0,\pi/2)\), describe all extensions of class \(C(\beta)\) of this operator, for \(\beta\in [\alpha,\pi/2]\).
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 1423194
zbMATH Keywords: \(C(\alpha)\)-suboperator
author: Yu M. Arlinskii
reviewed by: Radu Precup
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1423194