scholarly journals Multidimensional analogues of refined Bohr’s inequality

2020 ◽  
pp. 1 ◽  
Author(s):  
Ming-Sheng Liu ◽  
Saminathan Ponnusamy
Keyword(s):  
Bohr’S Inequality

scholarly journals Improved Bohr’s inequality for locally univalent harmonic mappings

2019 ◽  
Vol 30 (1) ◽  
pp. 201-213 ◽  
Author(s):  
Stavros Evdoridis ◽  
Saminathan Ponnusamy ◽  
Antti Rasila
Keyword(s):  
Harmonic Mappings ◽  
Bohr’S Inequality ◽  
Univalent Harmonic Mappings

ON BOHR'S INEQUALITY

2002 ◽  
Vol 85 (2) ◽  
pp. 493-512 ◽  
Author(s):  
VERN I. PAULSEN ◽  
GELU POPESCU ◽  
DINESH SINGH
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Banach Algebras ◽  
Equivalent Norm ◽  
C Algebra ◽  
Theoretic Proof ◽  
Higher Dimensional ◽  
Bohr’S Inequality ◽  
Kernel Hilbert Spaces ◽  
Multiplier Algebras

Bohr's inequality says that if $f(z) = \sum^{\infty}_{n = 0} a_n z^n$ is a bounded analytic function on the closed unit disc, then $\sum^{\infty}_{n = 0} \lvert a_n\rvert r^n \leq \Vert f\Vert_{\infty}$ for $0 \leq r \leq 1/3$ and that $1/3$ is sharp. In this paper we give an operator-theoretic proof of Bohr's inequality that is based on von Neumann's inequality. Since our proof is operator-theoretic, our methods extend to several complex variables and to non-commutative situations.We obtain Bohr type inequalities for the algebras of bounded analytic functions and the multiplier algebras of reproducing kernel Hilbert spaces on various higher-dimensional domains, for the non-commutative disc algebra ${\mathcal A}_n$, and for the reduced (respectively full) group C*-algebra of the free group on $n$ generators.We also include an application to Banach algebras. We prove that every Banach algebra has an equivalent norm in which it satisfies a non-unital version of von Neumann's inequality.2000 Mathematical Subject Classification: 47A20, 47A56.

scholarly journals Improved version of Bohr's inequality

2018 ◽  
Vol 356 (3) ◽  
pp. 272-277 ◽  
Author(s):  
Ilgiz R. Kayumov ◽  
Saminathan Ponnusamy
Keyword(s):  
Bohr’S Inequality

scholarly journals Bohr’s inequality for uniform algebras

2004 ◽  
Vol 132 (12) ◽  
pp. 3577-3579 ◽  
Author(s):  
Vern I. Paulsen ◽  
Dinesh Singh
Keyword(s):  
Uniform Algebras ◽  
Bohr’S Inequality

EXTENSIONS OF BOHR'S INEQUALITY

2006 ◽  
Vol 38 (06) ◽  
pp. 991-999 ◽  
Author(s):  
VERN I. PAULSEN ◽  
DINESH SINGH
Keyword(s):  
Bohr’S Inequality

scholarly journals About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 305
Author(s):  
Nicuşor Minculete
Keyword(s):  
Hilbert Space ◽  
Operator Theory ◽  
Schwarz Inequality ◽  
Linear Operators ◽  
Real Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Hilbert Space Operators ◽  
Bohr’S Inequality ◽  
Symmetric Shape

The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.

scholarly journals Bohr’s Inequality Revisited

2012 ◽  
pp. 279-290
Author(s):  
Masatoshi Fujii ◽  
Mohammad Sal Moslehian ◽  
Jadranka Mićić
Keyword(s):  
Bohr’S Inequality
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