Completely Bounded Maps and Operator Algebras

Selected Solutions from Vern Paulsen's book

I wrote up these solutions while learning about completely positive maps and completely bounded maps; operators spaces, systems and algebras. If you spot any mistakes (even a typo) please email me and I will fix it.

  1. Chapter 1. Introduction.
  2. Chapter 2. Positive Maps.
  3. Chapter 3. Completely Positive Maps.
  4. Chapter 4. Dilation Theorems.
  5. Chapter 5. Commuting Contractions.
  6. Chapter 6. Completely Positive Maps into M_n.
  7. Chapter 7. Arveson's Extension Theorems.
  8. Chapter 8. Completely Bounded Maps.
  9. Chapter 9. Completely Bounded Homomorphisms.
  10. Chapter 10. Polynomially Bounded Operators.
  11. Chapter 13. Operator Systems and Operator Spaces.
  12. Chapter 14. An Operator Space Bestiary.
  13. Chapter 15. Injective Envelopes.
  14. Chapter 16. Operator Algebras.