An Operator Extension of Bohr’s Inequality

An Operator Extension of Bohr's inequality

Generalizations of Bohr’s Inequality in Hilbert C∗-modules

We present a new operator equality in the framework of Hilbert C∗-modules. As a consequence, we get an extension of the Euler–Lagrange type identity in the setting of Hilbert bundles as well as several generalized operator Bohr’s inequalities due to O. Hirzallah, W.-S. Cheung–J.E. Pečarić and F. Zhang.

An Operator Extension of the Parallelogram Law and Related Norm Inequalities

We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr’s inequality and present several norm inequalities. More precisely, let A be a C∗ -algebra, T be a locally compact Hausdorff space equipped with a Radon measure μ and let (At)t∈T be a continuous field of operators in A such that the function t → At is norm c...

Multivariable Bohr Inequalities

Operator-valued multivariable Bohr type inequalities are obtained for: (i) a class of noncommutative holomorphic functions on the open unit ball of B(H)n, generalizing the analytic functions on the open unit disc; (ii) the noncommutative disc algebra An and the noncommutative analytic Toeplitz algebra F∞ n ; (iii) a class of noncommutative selfadjoint harmonic functions on the open unit ball of...

Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...