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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| Published in | Linear algebra and its applications Vol. 555; pp. 266 - 284 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
15.10.2018
American Elsevier Company, Inc |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Feki, Kais Baklouti, Hamadi Sid Ahmed, Ould Ahmed Mahmoud |
| Author_xml | – sequence: 1 givenname: Hamadi orcidid: 0000-0002-8557-1229 surname: Baklouti fullname: Baklouti, Hamadi email: h.baklouti@gmail.com organization: Sfax University, Tunisia – sequence: 2 givenname: Kais surname: Feki fullname: Feki, Kais email: kais.feki@hotmail.com organization: Sfax University, Tunisia – sequence: 3 givenname: Ould Ahmed Mahmoud surname: Sid Ahmed fullname: Sid Ahmed, Ould Ahmed Mahmoud email: sidahmed@ju.edu.sa organization: Aljouf University, Saudi Arabia |
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| Cites_doi | 10.1090/S0002-9939-99-05326-5 10.2140/pjm.1973.48.335 10.2307/2315737 10.1007/BF01212904 10.2140/pjm.1981.95.27 10.1007/s10474-005-0231-x 10.2140/pjm.1970.33.737 10.1090/S0002-9939-1952-0047004-9 10.1007/BF01292610 10.12732/ijpam.v112i4.6 10.1137/S0895479898343516 10.1080/03081089408818312 10.1016/j.laa.2010.09.012 10.1016/j.laa.2017.11.005 10.1090/S0002-9939-1966-0203464-1 10.1007/s00020-008-1613-6 10.1016/j.laa.2007.09.031 |
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| Title | Joint numerical ranges of operators in semi-Hilbertian spaces |
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