Non-commutative operator Bohr inequality

Hirzallah, Omar

doi:10.1016/s0022-247x(03)00185-9

Cited by 31 publications

(32 citation statements)

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“…e operator version of Bohr's inequality is �rst proved in [12,Corallary 1]. e following result gives a generalization of Bohr's inequality and also includes its reverse.…”

Section: Corollary 3 Let and If Is An Th-root Of Unity (Ie Andmentioning

confidence: 96%

“…e identities (12) and (13) become the parallelogram law when = and = = 2, respectively. e identities (12) and (13) …”

Section: Corollary 3 Let and If Is An Th-root Of Unity (Ie Andmentioning

confidence: 99%

“…e �rst version of operator Bohr's inequality was established via direct computations by Hirzallah [12]. Later, Hirzallah's results were extended by the same technique in [6,10,14].…”

Section: Introductionmentioning

confidence: 99%

“…e context of matrices is given in [5]. Bohr's inequality and related results were generalized to operator algebras in [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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An Order-Preserving Linear Map from Matrices to Banach *-Algebras and Applications

Chansangiam

2013

Journal of Mathematics

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We establish a theorem for which a number of absolute-value identities and inequalities in the framework of Banach * -algebras can be generated. To do this job, we construct an order-preserving linear map from the vector space of 2-by-2 hermitian matrices to a hermitian Banach * -algebras. is map can convert any suitable matrix ordering to a number of identities and inequalities in Banach * -algebras. Hence, we obtain a number of analogues of the well-known results in a framework of hermitian Banach * -algebras.

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“…e operator version of Bohr's inequality is �rst proved in [12,Corallary 1]. e following result gives a generalization of Bohr's inequality and also includes its reverse.…”

Section: Corollary 3 Let and If Is An Th-root Of Unity (Ie Andmentioning

confidence: 96%

“…e identities (12) and (13) become the parallelogram law when = and = = 2, respectively. e identities (12) and (13) …”

Section: Corollary 3 Let and If Is An Th-root Of Unity (Ie Andmentioning

confidence: 99%

“…e �rst version of operator Bohr's inequality was established via direct computations by Hirzallah [12]. Later, Hirzallah's results were extended by the same technique in [6,10,14].…”

Section: Introductionmentioning

confidence: 99%

“…e context of matrices is given in [5]. Bohr's inequality and related results were generalized to operator algebras in [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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An Order-Preserving Linear Map from Matrices to Banach *-Algebras and Applications

Chansangiam

2013

Journal of Mathematics

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“…10-13. Hirzallah 10 first established this inequality in the context of Hilbert space operators. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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Chansangiam¹

2010

ScienceAsia

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The classical Bohr inequality states that for complex numbers a, b and real numbers p, q > 1 such that 1/p + 1/q = 1, we have |a + b| 2 p|a| 2 + q|b| 2 with equality if and only if b = (p − 1)a. Various generalizations of the Bohr inequality occur for scalars, vectors, matrices and operators. In this paper, this inequality is generalized from Hilbert space operators to the context of C * -algebras and some extensions and related inequalities are obtained. For each inequality, the necessary and sufficient condition for the equality is also determined. The idea of transforming problems in operator theory to problems in matrix theory, which are easy to handle, plays a key role.

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