Hardy type inequaltiy for reproducing Kernel Hilbert space operators and related problems

Garayev, Mübariz T.; Gürdal, Mehmet; Saltan, Suna

doi:10.1007/s11117-017-0489-6

Cited by 33 publications

(12 citation statements)

References 11 publications

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“…So, it is natural to investigate Ber (A) and ber (A) for operators A ∈ B(H). For more detail informations about the Berezin set, Berezin number and their relations with the numerical range and numerical radius, the reader can be found in Karaev [14], Garayev et al [8], Garayev et al [9], Garayev et al [13], Gürdal et al [11], Gürdal et al [12], Yamancı et al [16], Altwaijry et al [10], and Garayev [7].…”

Section: Theorem 1 (Kantorovich Inequality) Let a Be A Positive Operator On A Hilbert Space H Such That M ≥mentioning

confidence: 99%

Some operator inequalities associated with Kantorovich and Hölder–McCarthy inequalities and their applications

BAŞARAN¹,

Gürdal²,

Güncan³

2019

Turk J Math

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Section: Theorem 1 (Kantorovich Inequality) Let a Be A Positive Operator On A Hilbert Space H Such That M ≥mentioning

confidence: 99%

Some operator inequalities associated with Kantorovich and Hölder–McCarthy inequalities and their applications

BAŞARAN¹,

Gürdal²,

Güncan³

2019

Turk J Math

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“…The Berezin number of an operator A is denoted by ber(A) and defined on a reproducing kernel Hilbert space H(Ω). Indeed, for any A ∈ B(H(Ω)), 0 ≤ ber(A) ≤ ω(A) ≤ A and if ber(A) = 0, then the following inequality for n ∈ N (see Garayev et al [8]) ber(A n ) ≤ ( w(A) ber(A)…”

Section: Introductionmentioning

confidence: 99%

Numerical radius and Berezin number inequality

Majee¹,

Maji²,

Manna³

2022

Preprint

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We study various inequalities for numerical radius and Berezin number of a bounded linear operator on a Hilbert space. It is proved that the numerical radius of a pure two-isometry is 1 and the Crawford number of a pure two-isometry is 0. In particular, we show that for any scalar-valued non-constant inner function θ, the numerical radius and the Crawford number of a Toeplitz operator T θ on a Hardy space is 1 and 0, respectively. It is also shown that numerical radius is multiplicative for a class of isometries and submultiplicative for a class of commutants of a shift. We have illustrated these results with some concrete examples. Finally, some Hardy-type inequalities for Berezin number of certain class of operators are established with the help of the classical Hardy's inequality.

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“…In this article, motivated mainly by the paper [34], we will prove some new inequalities for the Berezin number of powers of operators by using Kantorovich and Kantorovich type inequalities and also a refinement of Schwarz inequality due to Dragomir [10]. For the related results, the reader can see in [4,5,13,15,16,17,18,21,25,26,30,32,33,36,40,41,42,44]…”

Section: Introduction Notation and Preliminariesmentioning

confidence: 99%