OPERATORS IN L(L2a(D)) AND THE ASSOCIATED SYMBOLS

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Namita Das^†

 Let D = {z G C : |z| < 1} and L^^a (D)) be the space of all bounded linear operators from the Bergman space L²_a (D) into itself. In this paper we shall associate symbols to bounded linear operators in L(L²_a (D)) and analyse if a symbol calculus can be obtained.

MSC: 47B35, 32M15

Keywords: Toeplitz operators, Berezin transform, reproducing kernel, bounded harmonic functions, Bergman space.

DOI              10.56082/annalsarscimath.2024.1.97

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^†namitadas440@yahoo.co.in P.G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, 751004, Odisha, India

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PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 16 no 1, 2024