Operator inequalities in reproducing kernel Hilbert spaces

Authors : Ulas YAMANCİ

Pages : 204-211

Doi:10.31801/cfsuasmas.926981

View : 16 | Download : 11

Publication Date : 2022-03-30

Article Type : Research Paper

Abstract :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 $berinsert ignore into journalissuearticles values(A);$ for some self-adjoint operators $A$ on ${H}insert ignore into journalissuearticles values(\Omega );$.  Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that $insert ignore into journalissuearticles values(berinsert ignore into journalissuearticles values(A););^{n}\leq C_{1}berinsert ignore into journalissuearticles values(A^{n});$ for any positive operator $A$ on ${H}insert ignore into journalissuearticles values(\Omega );$.
Keywords : Mulholland type inequality, Berezin number, positive operator, reproducing kernel Hilbert space, Berezin symbol