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Remarks on the numerical range with respect to a family of projections
Author(s) -
Dada Waed,
Kerner Joachim
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710395
Subject(s) - numerical range , hilbert space , range (aeronautics) , mathematics , hausdorff space , bounded function , numerical analysis , toeplitz matrix , numerical stability , pure mathematics , mathematical analysis , materials science , composite material
In this note we report on the recently introduced concept of the numerical range of a bounded linear operator on a Hilbert space with respect to a family of projections. The importance of this new concept lies in the fact that it unifies and generalizes well‐established versions of the numerical range such as the classical numerical range introduced by Toeplitz and Hausdorff, the quadratic numerical range as well as the block numerical range. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)