Extensions of Euclidean operator radius inequalities

Abstract

To extend the Euclidean operator radius, we define w p for an n-tuplesfor p ≥ 1. We generalize some inequalities including Euclidean operator radius of two operators to those involving w p . Further we obtain some lower and upper bounds for w p . Our main result states that if f and g are nonnegative continuous functions on [0, ∞) satisfying f (t) g (t) = t for all t ∈ [0, ∞), then w rp p (

On Some Inequalities for the Generalized Euclidean Operator Radius

“…which refine the right hand side of (1.4). Clearly, all above mentioned inequalities generalize and refine some inequalities obtained in [20]. For recent inequalities, counterparts, refinements and other related properties concerning the generalized Euclidean operator radius the reader my refer to [5], [9] , [12], [13], [21], [23] and [24].…”

“…Basic properties of the generalized Euclidean operator radius. Moslehian et al [20], mention without proofs the following properties of the generalized Euclidean operator radius:…”

“…Despite of the authors in [20], mentioned the above basic properties of the generalized Euclidean operator radius, but it seems they missed some other important properties, rather than they left these properties without proof. Sometimes, it's nice to elaborate the proof of these elementary facts.…”

Hypo-<em>q</em>-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces

“…In 2012, [6] (see also [7] and [8]) the author have introduced the concept of s-q-numerical radius of an n-tuple of operators (T 1 ; : : : ; T n ) for q 1 as and established various inequalities of interest. For more recent results see also [10] and [12].…”

Hypo-<em>q</em>-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces

“…We use the following elementary inequalities for the nonnegative numbers a j , j = 1; :::; n and r q > 0 (see for instance [22] and [17])…”