Inequalities for generalized Euclidean operator radius via Young's inequality

On Some Inequalities for the Generalized Euclidean Operator Radius

“…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].…”

Upper bounds for numerical radius inequalities involving off-diagonal operator matrices

“…Now, we are in position to demonstrate the main results of this section by using some ideas from [2,13].…”

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

“…Proof. We use the following elementary inequalities for the nonnegative numbers a j , j = 1; :::; n and r q > 0 (see for instance [12]) Also, if we take q = 1 and r 1 in (2.32) and (2.33), then we get Proof. Let j = 1 n 1=p for j 2 f1; :::; ng ; then P n j=1 j j j p = 1: Therefore by (1.8) we get k(T 1 ; : : : ; T n )k h;n;q = sup k k n;p 1…”

“…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].…”