Further refinements of generalized numerical radius inequalities for\n Hilbert space operators

2018/05/19 by Monire Hajmohamadi, Hajmohamadi, Monire, Rahmatollah Lashkaripour +3
Engineering · Mathematics · #FOS: Mathematics #Fatigue and fracture mechanics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Structural Behavior of Reinforced Concrete

paper · pdf · doi:10.48550/arxiv.1805.07596

openalex publication_date 2018/05/19 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we show some refinements of generalized numerical radius\ninequalities involving the Young and Heinz inequalities. In particular, we\npresent\n nw_p^p(A₁^*T₁B₁,...,A_n^*T_nB_n)
leq
fracn^1-
frac1r2^
frac1r
Big
|
sum_i=1ⁿ[B_i^*\nf²(|T_i|)B_i]^rp+[A_i^*g²(|T_i^*|)A_i]^rp
Big
|^
frac1r\n-
inf
_|x
|=1
eta(x), where T_i, A_i, B_i \∈ mathbb\nB( mathscr H) , ,(1\≤ i\≤ n), f and g are nonnegative continuous\nfunctions on [0, \∞) satisfying f(t)g(t)=t for all t\∈ [0, \∞),\np, r\≥ 1, N\∈ mathbb N and \
eta(x)=\n
frac12
sum_i=1ⁿ
sum_j=1^N
Big(
sqrt[2^j]
langle\n(A_i^*g²(|T_i^*|)A_i)^px, x
rangle^2^j-1-k_j
langle\n(B_i^* f²(|T_i|)B_i)^px, x
rangle^k_j
quad-
sqrt[2^j]\n
langle (B_i^*f²(|T_i|)B_i)^px, x
rangle^k_j+1
langle\n(A_i^* g²(|T_i^*|)A_i)^px, x
rangle^2^j-1-k_j-1
Big)².\n n

Related

• An estimate for the numerical radius of the Hilbert space operators and a numerical radius inequality
• More accurate numerical radius inequalities
• Further Inequalities for the Numerical Radius of Hilbert Space Operators
• More accurate numerical radius inequalities (I)
• Generalized numerical radius and related inequalities