Geodesic
Operator valued analogues of multidimensional Bohr’s inequality
Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1020-1035

Voir la notice de l'article provenant de la source Cambridge

DOI

Let $\mathcal {B}(\mathcal {H})$ be the algebra of all bounded linear operators on a complex Hilbert space $\mathcal {H}$. In this paper, we first establish several sharp improved and refined versions of the Bohr’s inequality for the functions in the class $H^{\infty }(\mathbb {D},\mathcal {B}(\mathcal {H}))$ of bounded analytic functions from the unit disk $\mathbb {D}:=\{z \in \mathbb {C}:|z|<1\}$ into $\mathcal {B}(\mathcal {H})$. For the complete circular domain $Q \subset \mathbb {C}^{n}$, we prove the multidimensional analogues of the operator valued Bohr-type inequality which can be viewed as a special case of the result by G. Popescu [Adv. Math. 347 (2019), 1002–1053] for free holomorphic functions on polyballs. Finally, we establish the multidimensional analogues of several improved Bohr’s inequalities for operator valued functions in Q.
DOI : 10.4153/S0008439521001077
Mots-clés : Bohr radius, complete circular domain, homogeneous polynomial, operator valued analytic functions 
Allu, Vasudevarao; Halder, Himadri. Operator valued analogues of multidimensional Bohr’s inequality. Canadian mathematical bulletin, Tome 65 (2022) no. 4, pp. 1020-1035. doi: 10.4153/S0008439521001077
@article{10_4153_S0008439521001077,
     author = {Allu, Vasudevarao and Halder, Himadri},
     title = {Operator valued analogues of multidimensional {Bohr{\textquoteright}s} inequality},
     journal = {Canadian mathematical bulletin},
     pages = {1020--1035},
     year = {2022},
     volume = {65},
     number = {4},
     doi = {10.4153/S0008439521001077},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521001077/}
}
TY  - JOUR
AU  - Allu, Vasudevarao
AU  - Halder, Himadri
TI  - Operator valued analogues of multidimensional Bohr’s inequality
JO  - Canadian mathematical bulletin
PY  - 2022
SP  - 1020
EP  - 1035
VL  - 65
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439521001077/
DO  - 10.4153/S0008439521001077
ID  - 10_4153_S0008439521001077
ER  - 
%0 Journal Article
%A Allu, Vasudevarao
%A Halder, Himadri
%T Operator valued analogues of multidimensional Bohr’s inequality
%J Canadian mathematical bulletin
%D 2022
%P 1020-1035
%V 65
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439521001077/
%R 10.4153/S0008439521001077
%F 10_4153_S0008439521001077

Cité par Sources :