2006/01/30 by J. A. VIRTANEN, Jani A. Virtanen
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Spectral Theory in Mathematical Physics
paper · doi:10.1112/s0024609305018060
The Fredholm properties of Toeplitz operators Ta on Hardy spaces Tp (1 < p < ∞) with continuous symbols a are well understood. We consider Ta acting on H1, where the operator is bounded provided that a belongs to the class of symbols given by Janson and Stegenga's result on the pointwise multipliers on H1. A necessary and sufficient condition for Ta to be a Fredholm operator is given when a is continuous and satisfies a mild additional condition (much weaker than Hölder continuity). A formula for the index of Ta is also derived. In addition, we study the case of matrix-valued symbols and Toeplitz operators on BMOA. 2000 Mathematics Subject Classification 47B35, 47A53 (primary), 45E10, 30D50 (secondary).