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new lower bound for numerical radius for off-diagonal 2 × 2 matrices
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نویسنده
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moosavi b. ,shah hosseini m.
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منبع
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journal of linear and topological algebra - 2024 - دوره : 13 - شماره : 1 - صفحه:13 -18
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چکیده
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new norm and numerical radius inequalities for operators on hilbert space are given. among other inequalities, we prove that if $ a, b in b(h) $, then [vert a vert - frac{3 vert a-b^* vert }{2} leq omegaleft(left[begin{array}{cc} 0 a b 0 end{array}right]right).] moreover, $omega(ab) leq frac{3}{2} vert im(a) vert vert b vert + d_{b}; omega(a) $. in particular, if $ a $ is self-adjointable, then $omega(ab) leq d_{b} vert a vert$, where $d_{b}=underset{lambda in mathbb{c}}{mathop{inf}},left| b-lambda i right|$.
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کلیدواژه
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hilbert space ,norm inequality ,numerical radius ,bounded linear operator
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آدرس
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islamic azad university, safadasht branch, department of mathematics, iran, islamic azad university, shahr-e-qods branch, department of mathematics, iran
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پست الکترونیکی
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mohsen_shahhosseini@yahoo.com
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Authors
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