Joint numerical ranges of operators in semi-Hilbertian spaces

In this paper we aim to investigate the concept of numerical range and maximal numerical range relative to a positive operator of a d-tuple of bounded linear operators on a Hilbert space. Some properties and applications of these sets are studied. Mainly, it is proved that they are convex for d=1, t...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 555; pp. 266 - 284
Main Authors Baklouti, Hamadi, Feki, Kais, Sid Ahmed, Ould Ahmed Mahmoud
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.10.2018
American Elsevier Company, Inc
Subjects
Convexity
Hilbert space
Joint numerical range
Linear algebra
Linear operators
Maximal numerical range
Numerical analysis
Positive operator
Theorems
secondary
Joint numerical range
Convexity
primary
Positive operator
Maximal numerical range
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Summary:In this paper we aim to investigate the concept of numerical range and maximal numerical range relative to a positive operator of a d-tuple of bounded linear operators on a Hilbert space. Some properties and applications of these sets are studied. Mainly, it is proved that they are convex for d=1, this generalizes the well known Toeplitz–Hausdorff Theorem [24,16] and Stampfli's result [23]. Moreover, under additional hypotheses, we show that these sets are convex for d≥2.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.06.021