Surveys in Mathematics and its Applications
ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 6 (2011), 195 -- 202FINITE RANK INTERMEDIATE HANKEL OPERATORS ON THE BERGMAN SPACE
Namita Das
Abstract. In this paper we characterize the kernel of an intermediate Hankel operator on the Bergman space in terms of the inner divisors and obtain a characterization for finite rank intermediate Hankel operators.
2010 Mathematics Subject Classification: 32A36; 47B35.
Keywords: Hankel operators; Bergman space.
References
N. Das, The kernel of a Hankel operator on the Bergman space, Bull. London Math. Soc. 31 (1999), 75-80. MR1651001(99j:47034). Zbl 0942.47015.
P. L. Duren, D. Khavinson, H.S. Shapiro and C. Sundberg, Contractive zero-divisors in Bergman spaces, Pacific J. Math. 157 (1993), 37-56. MR1197044(94c:30048). Zbl 0739.30029.
P.L. Duren, D. Khavinson, H. S. Shapiro and C. Sundberg, Invariant subspaces in Bergman spaces and the biharmonic equation, Michigan Math. J. 41 (1994), 247-259. MR1278431(95e:46030). Zbl 0833.46044.
H. Hedenmalm, A factorization theorem for square area-integrable analytic functions, J. Reine. Angew. Math. 422 (1991), 45-68. MR1133317(93c:30053). Zbl 0734.30040.
B. Korenblum and M. Stessin, On Toeplitz-invariant subspaces of the Bergman space, J. Funct. Anal. 111 (1993), 76-96. MR1200637(94f:30049). Zbl 0772.30042.
E. Strouse, Finite rank intermediate Hankel operators, Arch. Math. (Basel) 67 (1996), 142-149. MR1399831(97i:47047). Zbl 0905.47014.
K. Zhu, Operator theory in function spaces, Monographs and Textbooks in Pure and Applied Mathematics, Marcell Dekker, Inc. 139, New York and Basel, 1990. MR1074007(92c:47031). Zbl 0706.47019.
Namita Das
P. G. Dept. of Mathematics,
Utkal University, Vanivihar, Bhubaneswar,
751004, Orissa, India.
e-mail: namitadas440@yahoo.co.in