Math 546 Hilbert spaces


Time/Location: MWF, 1-1.50 pm, Altgeld 441

Instructor: Marius Junge, Altgeld  363,  Office hour, Wednesday 5-6 pm.

Text:  John B. Conway,   A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. 

          Additional text:  , John B. Conway  A course in functional analysis. Second edition. Graduate Text in  Mathematics, 96. Springer-Verlag, New York, 1990.


Plan:                                                                                                             Course hotline (email to students and instructor)

Elementary Hilbert space theory:  Existence of ONB, Duality, weak toplogies                               Courses webpage

Holmorphic Functional Calculus for Banach and C*-algebras:  Banachalg,  Spectrum
 holomorphic functional calculus     continuous functional calculus    Approximate unit                                           Department of Mathematics

Functional Calculus for von Neumann algebras and the double commutant theorem                  
weak topologies   projections valued measures,  a density Lemma ,  a multiplicativity  Lemma
 from C(K) to measurable,  more on normal, cyclic vectors, separable case

Applications                                                                                      Presentations:
Double commutant, Polar decomposition, Irreducible representations, More on Ideals
Universal representation, Normal States                                      Hassler, Ackermann, Longfield, Rezvani, Qu Lu, Nata Wat, Yuhze Wang, Wang Wu,Min Zao

Grading: Homework (50%) and presentation (50%)                      hw1,hw2,hw3,hw4,hw5,hw6,hw7,hw8,hw9,hw10,hw11,hw12,   a solution

Topics:   Commuting approximate unit (C.), Stabilization (Se.), Kaplanski (St), Index (Min),  Application of Stinespring (Ja) ,  Operator Monotone (Nat,)