Using a refinement of the classical Young inequality, we refine some inequalities of operators including the function ωp, where ωp is defined for p⩾1 and operators T1,…,Tn∈B(H) ...byωp(T1,…,Tn):=sup‖x‖=1(∑i=1n|〈Tix,x〉|p)1p. Among other things, we show that if T1,…,Tn∈B(H) and p≥q≥1 with 1p+1q=1, then1n‖∑i=1nTi‖2≤ωp(|T1|,…,|Tn|)ωq(|T1⁎|,…,|Tn⁎|)1n‖∑i=1nTi‖2≤1p‖∑i=1n|Ti|p‖+1q‖∑i=1n|Ti⁎|q‖−inf‖x‖=‖y‖=1δ(x,y), where δ(x,y)=1p(∑i=1n〈|Ti|x,x〉p−∑i=1n〈|Ti⁎|y,y〉q)2.
In this paper, we introduce the
-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the
-operator radius. The properties of the newly defined radius ...are discussed, emphasizing how it extends some known results in the literature.
Some extended numerical radius inequalities Sahoo, Satyajit; Rout, Nirmal Chandra; Sababheh, Mohammad
Linear & multilinear algebra,
04/2021, Letnik:
69, Številka:
5
Journal Article
Recenzirano
The main goal of this article is to present generalized extensions of numerical radius inequalities involving the Euclidean operator radius and the numerical radius of some well-known operator ...quantities such as Heinz means, arithmetic mean and f-connection.
In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequality. In particular, we present
where
,
and
are nonnegative continuous ...functions on
satisfying
for all
,
,
, and
This paper proves several new inequalities for the Euclidean operator radius, which refine some recent results. It is shown that the new results are much more accurate than the related, recently ...published results. Moreover, inequalities for both symmetric and non-symmetric Hilbert space operators are studied.
In this work, we present some new upper and lower bounds for the Euclidean operator radius of a pair of Hilbert space operators. Some of these bounds refine certain existing ones. As applications of ...these results, we provide some new bounds for the classical numerical radius.
In the literature, there are many criteria to generalize the concept of a numerical radius; one of the most recent and interesting generalizations is the so-called generalized Euclidean operator ...radius, which reads: ωpT1,⋯,Tn:=supx=1∑i=1nTix,xp1/p,p≥1, for all Hilbert space operators T1,⋯,Tn. Simply put, it is the numerical radius of multivariable operators. This study establishes a number of new inequalities, extensions, and generalizations for this type of numerical radius. More precisely, by utilizing the mixed Schwarz inequality and the extension of Furuta’s inequality, some new refinement inequalities are obtained for the numerical radius of multivariable Hilbert space operators. In the case of n=1, the resulting inequalities could be considered extensions and generalizations of the classical numerical radius.
In this paper, we prove that if
,
> 0 and 0 ≤ α ≤ 1, then for
= 1, 2, 3, . . . ,
where
= min{α, 1 – α }. This is a considerable new generalization of two refinements of the Young inequality due to ...Kittaneh and Manasrah, and Hirzallah and Kittaneh, which correspond to the cases
= 1 and
= 2, respectively. As applications we give some refined Young type inequalities for generalized euclidean operator radius and the numerical radius of some well-know
-connection of operators and refined some Young type inequalities for the traces, determinants, and norms of positive definite matrices.
In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian ...decomposition of a given Hilbert space operator are proven.
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