Welcome to the InfoSci Platform
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

Ulaş Yamancı, Mehmet Gürdal
Copyright: © 2020 |Pages: 24
ISBN13: 9781799801344|ISBN10: 1799801349|ISBN13 Softcover: 9781799801351|EISBN13: 9781799801368
DOI: 10.4018/978-1-7998-0134-4.ch004
Cite Chapter Cite Chapter

MLA

Yamancı, Ulaş, and Mehmet Gürdal. "Berezin Number Inequalities of an Invertible Operator and Some Slater Type Inequalities in Reproducing Kernel Hilbert Spaces." Emerging Applications of Differential Equations and Game Theory, edited by Sırma Zeynep Alparslan Gök and Duygu Aruğaslan Çinçin, IGI Global, 2020, pp. 55-78. https://doi.org/10.4018/978-1-7998-0134-4.ch004

APA

Yamancı, U. & Gürdal, M. (2020). Berezin Number Inequalities of an Invertible Operator and Some Slater Type Inequalities in Reproducing Kernel Hilbert Spaces. In S. Alparslan Gök & D. Aruğaslan Çinçin (Eds.), Emerging Applications of Differential Equations and Game Theory (pp. 55-78). IGI Global. https://doi.org/10.4018/978-1-7998-0134-4.ch004

Chicago

Yamancı, Ulaş, and Mehmet Gürdal. "Berezin Number Inequalities of an Invertible Operator and Some Slater Type Inequalities in Reproducing Kernel Hilbert Spaces." In Emerging Applications of Differential Equations and Game Theory, edited by Sırma Zeynep Alparslan Gök and Duygu Aruğaslan Çinçin, 55-78. Hershey, PA: IGI Global, 2020. https://doi.org/10.4018/978-1-7998-0134-4.ch004

Export Reference

Mendeley
Favorite

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.

Request Access

You do not own this content. Please login to recommend this title to your institution's librarian or purchase it from the IGI Global bookstore.