IRMA-International.org: Creator of Knowledge
Information Resources Management Association
Advancing the Concepts & Practices of Information Resources Management in Modern Organizations

Berezin Number Inequalities of an Invertible Operator and Some Slater Type Inequalities in Reproducing Kernel Hilbert Spaces

Berezin Number Inequalities of an Invertible Operator and Some Slater Type Inequalities in Reproducing Kernel Hilbert Spaces
View Sample PDF
Author(s): Ulaş Yamancı (Süleyman Demirel University, Turkey)and Mehmet Gürdal (Süleyman Demirel University, Turkey)
Copyright: 2020
Pages: 24
Source title: Emerging Applications of Differential Equations and Game Theory
Source Author(s)/Editor(s): Sırma Zeynep Alparslan Gök (Süleyman Demirel University, Turkey)and Duygu Aruğaslan Çinçin (Süleyman Demirel University, Turkey)
DOI: 10.4018/978-1-7998-0134-4.ch004

Purchase


Abstract

A reproducing kernel Hilbert space (shorty, RKHS) H=H(Ω) on some set Ω is a Hilbert space of complex valued functions on Ω such that for every λ∈Ω the linear functional (evaluation functional) f→f(λ) is bounded on H. If H is RKHS on a set Ω, then, by the classical Riesz representation theorem for every λ∈Ω there is a unique element kH,λ∈H such that f(λ)=〈f,kH,λ〉; for all f∈H. The family {kH,λ:λ∈Ω} is called the reproducing kernel of the space H. The Berezin set and the Berezin number of the operator A was respectively given by Karaev in [26] as following Ber(A)={A(λ):λ∈Ω} and ber(A):=|A(λ)|. In this chapter, the authors give the Berezin number inequalities for an invertible operator and some other related results are studied. Also, they obtain some inequalities of the slater type for convex functions of selfadjoint operators in reproducing kernel Hilbert spaces and examine related results.

Related Content

Pawan Kumar, Mukul Bhatnagar, Sanjay Taneja. © 2024. 26 pages.
Kapil Kumar Aggarwal, Atul Sharma, Rumit Kaur, Girish Lakhera. © 2024. 19 pages.
Mohammad Kashif, Puneet Kumar, Sachin Ghai, Satish Kumar. © 2024. 15 pages.
Manjit Kour. © 2024. 13 pages.
Sanjay Taneja, Reepu. © 2024. 19 pages.
Jaspreet Kaur, Ercan Ozen. © 2024. 28 pages.
Hayet Kaddachi, Naceur Benzina. © 2024. 25 pages.
Body Bottom