In this work, some generalized Euclidean operator radius inequalities are established. Refinements of well-known results provided. Among others, bounds in terms the Cartesian decomposition a given Hilbert space proven.

An operator T is called (α, β)-normal (0 ≤ α ≤ 1 ≤ β) if αT ∗T ≤ TT ∗ ≤ βT ∗T. In this paper, we establish various inequalities between the operator norm and its numerical radius of (α, β)-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.

We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space X. This is done by finite dimensional approximation. In particular we prove Logarithmic-Sobolev and Poincaré inequalities, and thanks to these inequalities we deduce spectral properties of the OrnsteinUhlenbeck operator. 2010 Mathematics Subjec...

We prove pointwise inequalities for the maximal operator over all the directions in R when acting on l-radial functions and on product functions. From these inequalities we deduce boundedness results on L for p > n; these can be applied to other operators, in particular to the Kakeya maximal operator.