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Royal road theorem
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Classroom Contents
Monotonicity, Convexity, and Realization of Noncommutative Functions
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- 1 Intro
- 2 Classical motivation
- 3 Goals of the talk
- 4 Representation of Pick functions
- 5 Connection with positive matrices
- 6 Matrix inequalities
- 7 The functional calculus
- 8 Special matrix functions
- 9 Classical representations: Löwner-Nevanlinna
- 10 Classical representations: Kraus
- 11 Thematic ideas in classical proofs
- 12 The matrix universe (more usual)
- 13 Noncommutative sets
- 14 Noncommutative functions
- 15 nc matrix functions
- 16 Löwner's Theorem
- 17 free Nevanlinna representation
- 18 What is the royal road?
- 19 Royal road approach
- 20 A royal road: dominions
- 21 Royal road theorem
- 22 Proof idea
- 23 A road to realizations
- 24 Convex functions
- 25 Kraus theorem
- 26 The butterfly realization
- 27 Further considerations
