Joint numerical ranges of operators in semi-Hilbertian spaces

• Published in: Linear algebra and its applications Vol. 555; pp. 266 - 284
• Main Authors: Baklouti, Hamadi, Feki, Kais, Sid Ahmed, Ould Ahmed Mahmoud
• Format: Journal Article
• Language: English
• 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

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...