Namita Das, Swarupa Roy†
Abstract: In this paper we have shown that if (L2 h(dA )) L (D) and RangeT( ) is closed, then the Toeplitz operator T( ) LL2 a(dA ) is a Fredholm operator of index zero and T( ) is not of nite rank. Several applications of the result were also obtained. We further show that if LMn (D) is such that T is Fredholm and of index zero in LL2Cn a (dA ) thenthereexists En n =E MnsuchthatT+ is invertible for all su ciently small nonzero . Here E is a total subspace of L (D) and Mn is the set of all n n matrices with complex entries.
MSC: 47B38, 47B32
keywords: Weighted Bergman spaces, Finite rank operator, Toeplitz operator, Little Hankel operator, Bounded harmonic functions.
DOI 10.56082/annalsarscimath.2021.1-2.178
†namitadas440@yahoo.co.in P. G. Dept. of Mathematics, P. G. Dept. of Mathematics, Utkal University,Vani Vihar, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
swarupa.roy@gmail.com P. G. Dept. of Mathematics, P. G. Dept. of Mathematics, Utkal University,Vani Vihar, Utkal University, Vani Vihar, Bhubaneswar- 751004, Odisha, India
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 13 no 1-2, 2021
