International Science and Technology Journal
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Under supervision of
Open Access Journal
ISSN: 2519-9854 (Online)
ISSN: 2519-9846 (Print)
A peer-reviewed and open access journal concerned with publishing researches and studies in the field of applied sciences and engineering
SOME RESULTS ON THE POINT NUMERICAL RANGE OF AN . N. TUPLE OF OPERATORS ON ASEMI-INNER PRODUCT SPACE
| Researcher(s): | - Mohamed Mohamed Elgezzon
- Moamar Mohamed Alamari
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| Institution: | المعهد العالي للتقنيات الهندسية زليتن |
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| Field: | |
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| Published in: | 9th volume - December 2016 |
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الملخص
من الحقائق المعروفة في هذا الموضوع هي المبرهنة المتعلقة بالقيم الذاتية (Eigen Values) للمؤثر T (حيث T B(H)، Hهو فضاء هلبرت)، والتي تنص على أن:
مجموعة القيم الذاتية للمؤثر T هي مجموعة جزئية من المدى العددي W(T) للمؤثر T، وأن العكس يكون صحيحاً بشرط أن : || = ||T|| .
Abstract
P.R. Halmos [3] has proved that. For any bounded operator T and a Hilbert space H, every eigen value of T is in the numerical range W(T), and the converse is true if ||=ווT וו.
In this paper we generalize the above result to the case of n-tuples of the operators on any normed linear space.
(semi-inner product space) with some necessary condition for the converse. Further, we improve a theorem of lumer [5] which asserts that : the approximate point spectrum (T) of T B(X), where X is any normed space is contained in (W(T)) ̅ where dash is denotes closure.