Generalizations of Bohr inequality for Hilbert space operators

Matrix Order in Bohr Inequality for Operators

The classical Bohr inequality says that |a+b| ≤ p|a|+q|b| for all scalars a, b and p, q > 0 with 1 p + 1 q = 1. The equality holds if and only if (p− 1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogr...

On an inequality for operators on Hilbert space

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

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.