Tensor Norms and Operator Ideals (Volume 176) (North-Holland Mathematics Studies, Volume 176)

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises. The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises. Content: Edited by Page iii Copyright page Page iv Introduction Pages 1-6 Andreas Defant, Klaus Floret Chapter I Basic Concepts Pages 7-145 Chapter II Tensor Norms Pages 146-364 Chapter III Special Topics Pages 365-488 Appendix A: Some Structural Properties of Banach Spaces Pages 489-526 Bibliography Pages 527-544 List of Symbols Pages 545-554 Index Pages 555-566 With chapters entitled Basic Concepts, Tensor Norms, and Special Topics, this work may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. Each section is accompanied by a series of exercises Shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. This work presents the theory of tensor norms as designed by Grothendieck in the Resume and deals with the relation between tensor norms and operator ideals.