On the Joint A-Numerical Radius of Operators and Related Inequalities

Abstract

In this paper, we study p-tuples of bounded linear operators on a complex Hilbert space with adjoint operators defined with respect to a non-zero positive operator A. Our main objective is to investigate the joint A-numerical radius of the p-tuple.We established several upper bounds for it, some of which extend and improve upon a previous work of the second author. Additionally, we provide several sharp inequalities involving the classical A-numerical radius and the A-seminorm of semi-Hilbert space operators as applications of our results.

Further Accurate Numerical Radius Inequalities

“…and this shows that our first two inequalities are much better than (11). Practically and more preciously, the first two inequalities in (20) are stronger than the upper bound in (3), and the inequalities in (9), (10), and (11).…”

“…As we can see, the first inequality turns into an equality in this example and gives the exact value of the numerical radius. Moreover, the second inequality improves the Sabaheh-Mordai inequality (11). Indeed, applying (11), we obtain…”

“…Moreover, the second inequality improves the Sabaheh-Mordai inequality (11). Indeed, applying (11), we obtain…”

“…In this work, further refinements of the previously mentioned inequalities are presented. Some new improvements and refinements purify the inequalities (4)- (11). The inequalities demonstrated in this work are not only an improvement over previous inequalities but also stronger than them.…”

“…The constant 1 32 is the best possible. For more generalizations, counterparts, and recent related results, the reader may refer to [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Further results can be found in [23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”