Toeplitz Operators and Index Theory in Several Complex Variables

1. Front Matter

   Pages i-xi

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2. Multi-variable Complex Analysis and Domains of Holomorphy

   • Harald Upmeier

   Pages 1-76

3. Harmonic Analysis on Hilert Spaces of Holomorphic Functions

   • Harald Upmeier

   Pages 77-174

4. Multiplier C* -Algebras and Their Representations

   • Harald Upmeier

   Pages 175-240

5. Toeplitz Operators and Toeplitz C*-Algebras

   • Harald Upmeier

   Pages 241-370

6. Index Theory for Multivariable Toeplitz Operators

   • Harald Upmeier

   Pages 371-461

7. Back Matter

   Pages 462-483

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4. 1 Bergman-Toeplitz Operators Over Bounded Domains 242 4. 2 Hardy-Toeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* -Algebras 4. 3 256 4. 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4. 5 Bergman-Toeplitz Operators Over Tubular Domains 278 4. 6 Hardy-Toeplitz Operators Over Polycircular Domains 284 4. 7 Bergman-Toeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* -Algebras 299 4. 9 Actions and Coactions on C* -Algebras 310 4. 10 Hardy-Toeplitz Operators Over K-circular Domains 316 4. 11 Hardy-Toeplitz Operators Over Symmetric Domains 325 4. 12 Bergman-Toeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 K-Theory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*-Algebras K-Theory for 394 5. 4 Index Theory for Symmetric Domains 400 5. 5 Index Theory for Tubular Domains 432 5. 6 Index Theory for Polycircular Domains 455 References 462 Index of Symbols and Notations 471 In trod uction Toeplitz operators on the classical Hardy space (on the I-torus) and the closely related Wiener-Hopf operators (on the half-line) form a central part of operator theory, with many applications e. g. , to function theory on the unit disk and to the theory of integral equations.

• Algebra
• Pseudoconvexity
• Variable
• calculus
• complex analysis
• function
• functional analysis
• geometry

• Department of Mathematics, University of Marburg, Marburg, Germany

  Harald Upmeier

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