Sharpened forms of an inequality of von Neumann
type: Item
instance of: scholarly article
title: Sharpened forms of an inequality of von Neumann
zbMATH Open document ID: 0631.47004
DOI: 10.1007/BF01168002
author: Ky Fan
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173812
review text: Let H be a complex Hilbert space. The inequality of von Neumann asserts that for a function f analytic on a neighbourhood of the closed unit disk \({\bar \Delta}\), if f(\({\bar \Delta}\))\(\subset \bar D\) then \(\| f(A)\| \leq 1\) for every bounded linear operator A on H. An equivalent result holds for the open unit disk with \(\leq\) replaced by \(<\). This paper proves a number of inequalities which improve on the latter version. One corollary yields a sharpened form of Schwarz's lemma (for operators).
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 4026161
zbMATH Keywords: inequality of von Neumann
zbMATH Keywords: Schwarz's lemma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4026161