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Toeplitz Operators with Symbols Generated by Slowly Oscillating and Semi-Almost Periodic Matrix Functions |
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| Authors: | Bastos, M. A. Karlovich, Yu. I. Silbermann, B. |
| Affiliation: | Departamento de Matemática, Instituto Superior Técnico Av. Rovisco Pais, 1049–001 Lisbon, Portugal. E-mail: abastos{at}math.ist.utl.pt Facultad de Ciencias Universidad Autónoma del Estado de Morelos Av. Universidad 1001, Col. Chamilpa, Cuernavaca, Morelos, Mexico. E-mail: karlovich{at}buzon.uaem.mx Fakultät für Mathematik, Technische Universität Chemnitz 09107 Chemnitz, Germany. E-mail: bsilberm{at}mathematik.tu-chemnitz.de |
| Abstract: | We develop the Fredholm theory for Toeplitz operators, withsymbols in the C*-algebra D = [SO, SAP]n, n generated by allslowly oscillating (SO) and semi-almost periodic (SAP) n x nmatrix functions, on the Hardy spaces  (with 1 < p <  ) over the upper half-plane.Using limit operator techniques, we get necessary Fredholm conditionsfor any operator in the Banach algebra alg(S, D) of singularintegral operators with coefficients in D on the space [Lp (R)]n.Applying the AllanDouglas local principle and the theoryof Toeplitz operators with SAP matrix symbols, we also establishFredholm criteria for Toeplitz operators with matrix symbolsg  D on the space . An index formula for Fredholm Toeplitz operators with matrix symbolsin D is obtained on the basis of an appropriate approximationof slowly oscillating components of the symbols. 2000 MathematicsSubject Classification 47B35 (primary), 47A53 (secondary). |
| Keywords: | Toeplitz operators slowly oscillating and semi-almost periodic matrix symbols Fredholm criteria index formula Hardy spaces |
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