Number of the records: 1
In search of convexity: Diagonals and numerical ranges
- 1.
SYSNO ASEP 0544892 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title In search of convexity: Diagonals and numerical ranges Author(s) Müller, Vladimír (MU-W) RID, SAI
Tomilov, Y. (PL)Source Title Bulletin of the London Mathematical Society. - : Wiley - ISSN 0024-6093
Roč. 53, č. 4 (2021), s. 1016-1029Number of pages 14 s. Language eng - English Country GB - United Kingdom Keywords convexity ; Hilbert space operator Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GX20-31529X GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000625165700001 EID SCOPUS 85101917684 DOI 10.1112/blms.12480 Annotation We show that the set of all possible constant diagonals of a bounded Hilbert space operator is always convex. This, in particular, answers an open question of Bourin (2003). Moreover, we show that the joint numerical range of a commuting operator tuple is, in general, not convex, which fills a gap in the literature. We also prove that the Asplund–Ptak numerical range (which is convex for pairs of operators) is, in general, not convex for tuples of operators. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1112/blms.12480
Number of the records: 1