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- W2064345859 abstract "Operator-valued multivariable Bohr type inequalities are obtained for: [(i)] a class of noncommutative holomorphic functions on the open unit ball of $B(mathcal {H})^n$, generalizing the analytic functions on the open unit disc; [(ii)] the noncommutative disc algebra $mathcal {A}_n$ and the noncommutative analytic Toeplitz algebra $F_n^infty$; [(iii)] a class of noncommutative selfadjoint harmonic functions on the open unit ball of $B(mathcal {H})^n$, generalizing the real-valued harmonic functions on the open unit disc; [(iv)] the Cuntz-Toeplitz algebra $C^*(S_1,ldots , S_n)$, the reduced (resp. full) group $C^*$-algebra $C_{red}^*(mathbb {F}_n)$ (resp. $C^*(mathbb {F}_n)$) of the free group with $n$ generators; [(v)] a class of analytic functions on the open unit ball of $mathbb {C}^n$. The classical Bohr inequality is shown to be a consequence of Fejérâs inequality for the coefficients of positive trigonometric polynomials and Haager- up-de la Harpe inequality for nilpotent operators. Moreover, we provide an inequality which, for analytic polynomials on the open unit disc, is sharper than Bohrâs inequality." @default.
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- W2064345859 date "2007-05-08" @default.
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- W2064345859 title "Multivariable Bohr inequalities" @default.
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