## Math 7330, Fall 2002

Ambar Sengupta, Office: Lockett 324, Phone: 578-1607

e-mail: sengupta@math.lsu.edu

Home: http://www.math.lsu.edu/~sengupta

Homework Assignments and Notes

Prerequisites: Measure and Integration [Math 7312], Topological Spaces,
Linear Algebra.

Textbook: Rudin's "Functional Analysis" will be a useful
reference.

Our objective will be to study the spectral theorem for operators on Hilbert
spaces. On the way, we shall study the Gelfand theory of commutative Banach
algebras.

There will be problem assignments, at least 50 percent of which must be
turned in to pass the class. Passing grades will be decided as follows: A for
excellent/distinguished performance, B for good performance, C for acceptable
work, D for poor.

##### Homework Assignments and Notes

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- Orthogonal projections.
- Homework 1: Spectral Theorem for Finite Dimensions
- Homework 2: Projection Operators and Projection-Operator-Valued Measures
- Notes/Homework 3: Banach Algebras
- Notes/Homework 4: Commutative Banach Algebras I
- Notes/Homework 5: Commutative Banach Algebras II
- Notes/Homework 6: Commutative Banach Algebras III
- Notes/Homework 7: The Spectral Theorem