Berezin number and numerical radius inequalities for operators on Hilbert spaces

Sahoo, Satyajit; Das, Namita; Mishra, Debasisha

doi:10.1007/s43036-019-00035-8

Cited by 17 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For our purpose, we set the Berezin norm of an operator as A ber supA kλ Therefore, the Berezin symbol uniquely determines the operator. Some excellent results about the Berezin number were found in [4,5,13,[25][26][27] very recently. Among many techniques in obtaining numerical radius and Berezin number inequalities is the study of certain scalar ones.…”

Section: Introductionmentioning

confidence: 90%

Some extended Berezin number inequalities

Sahoo

Bakherad

2021

Filomat

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 90%

Some extended Berezin number inequalities

Sahoo

Bakherad

2021

Filomat

Self Cite

View full text Add to dashboard Cite

show abstract

“…More information about numerical range and numerical radius can be found in [6,7,9,18,19,21]. Using the Hardy-Hilbert type inequalities and some well-known inequalities, some important results about the Berezin number inequalities were obtained in [2,3,10,22,[24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Operator inequalities in reproducing kernel Hilbert spaces

Yamancı¹

2022

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

View full text Add to dashboard Cite

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number ber(A) for some self-adjoint operators A on H(Ω). Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that (ber(A)) n ≤ C 1 ber(A n ) for any positive operator A on H(Ω).

show abstract

“…w ( T ) is the numerical radius of , which is defined as It is well-known that defines a norm on , and is equivalent to the usual operator norm In fact, for every , Extensive studies on different generalizations, refinements and applications of numerical radius inequalities have been conducted [ 3 , 21 , 22 , 30 , 38 – 40 ]. Saddi [ 36 ] introduced the A-numerical radius of T for , which is denoted as , and is defined as follows: It then follows that If and U is A -unitary, then .…”

Section: Introductionmentioning

confidence: 99%

On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

Kittaneh

Sahoo

2021

Ann. Funct. Anal.

Self Cite

View full text Add to dashboard Cite

The main goal of this article is to establish several new -numerical radius equalities for n × n circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where is the n × n diagonal operator matrix whose diagonal entries are positive bounded operator A. Some special cases of our results lead to the results of earlier works in the literature, which shows that our results are more general. Further, some pinching type -numerical radius inequalities for n × n block operator matrices are given. Some equality conditions are also given. We also provide a concluding section, which may lead to several new problems in this area.

show abstract

Berezin number and numerical radius inequalities for operators on Hilbert spaces

Cited by 17 publications

References 23 publications

Some extended Berezin number inequalities

Some extended Berezin number inequalities

Operator inequalities in reproducing kernel Hilbert spaces

On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

Contact Info

Product

Resources

About