Berezin number inequalities of operators on reproducing kernel Hilbert spaces

Sen, Anirban; Bhunia, Pintu; Paul, Kallol

doi:10.1216/rmj.2022.52.1039

Cited by 14 publications

(4 citation statements)

References 15 publications

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“…Notably, we observe that ber(I Λ ) = 1 and Tk µ , k µ ≤ ber(T) k µ 2 hold for all reproducing kernels k µ . Similar to ber(T), we found in [11] the following concept:…”

Section: Introductionsupporting

confidence: 70%

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A Generalized Norm on Reproducing Kernel Hilbert Spaces and Its Applications

Altwaijry

Feki

Minculete

2023

Axioms

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The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm of bounded linear operators that act on reproducing kernel Hilbert spaces. Through our analysis, we hoped to enhance the understanding of the properties and behavior of such operators and contribute to the development of new mathematical tools for their characterization and application.

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“…Notably, we observe that ber(I Λ ) = 1 and Tk µ , k µ ≤ ber(T) k µ 2 hold for all reproducing kernels k µ . Similar to ber(T), we found in [11] the following concept:…”

Section: Introductionsupporting

confidence: 70%

“…From relation (1), we have the upper bound of T α,β as α T 2 + βω 2 (T), and from relation (11) the upper bound T 2 max α, β + αβ T ω(T). Comparing the two upper bounds, we find…”

Section: Resultsmentioning

confidence: 99%

A Generalized Norm on Reproducing Kernel Hilbert Spaces and Its Applications

Altwaijry

Feki

Minculete

2023

Axioms

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“…It is clear from the definition that Ber(A) ⊆ W (A) and so ber(A) ≤ w(A). The Berezin symbols and Berezin number inequalities have been studied by many mathematicians over the years, for the latest and recent results we refer the readers to see [2,8,16,18,20,21,28,30] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Davis–Wielandt–Berezin radius inequalities of reproducing kernel Hilbert space operators

2023

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Several upper and lower bounds of the Davis-Wielandt-Berezin radius of bounded linear operators defined on a reproducing kernel Hilbert space are given. Further, an inequality involving the Berezin number and the Davis-Wielandt-Berezin radius for the sum of two bounded linear operators is obtained, namely, if A and B are reproducing kernel Hilbert space operators, thenwhere η(•) and ber(•) are the Davis-Wielandt-Berezin radius and the Berezin number, respectively.

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“…Observe that the above equality may not be true for selfadjoint operators. The Berezin number and Berezin norm inequalities have been studied by many mathematicians [8,21,22,33,36,38,43,44].…”

Section: Introductionmentioning

confidence: 99%