Abstract
AbstractLet
$\mathcal {B}(\mathcal {H})$
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.
Publisher
Canadian Mathematical Society
Cited by
8 articles.
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