Namita Das†, Madhusmita Sahoov†
Abstract: In this paper we introduce a class A L (D) such that if A and satis es certain positive-de nite condition, then there exists a A such that (z) e (z) for some constant > 0 Further, if (z) = Akz kz for some bounded positive, invertible operator A from the Bergman space L2 a(D) into itself then (z) = (logA)kz kz Here kz z D are the normalized reproducing kernel of L2 a(D) Applications of these results are also discussed.
2010 Mathematics Subject Classifcation: 32A36 ; 47B38.
keywords: Berezin transform, Bergman space, Invertible operators, Positive operators, Reproducing kernel.
DOI 10.56082/annalsarscimath.2021.1-2.70
†namitadas440@yahoo.co.in, P.G.Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India. …smita 782006@yahoo.co.in, School of Applied Sciences (Mathematics), KIIT Deemed to be University, Campus-3(Kathajori Campus), Bhubaneswar-751024, Odisha, India.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 13 no 1-2, 2021
