Unit · year 3
MU-304 · Functional Analysis
Threads space · structure5 theorems
Infinite-dimensional linear algebra and analysis on Banach and Hilbert spaces.
Theorems in this unit
T-095
The Hahn–Banach theorem
Bounded functionals extend without increasing norm.
T-096
The open mapping theorem
A surjective bounded operator between Banach spaces is open.
T-097
The closed graph theorem
A closed-graph operator between Banach spaces is bounded.
T-098
The uniform boundedness principle
Pointwise-bounded families of operators are uniformly bounded.
T-099
The Riesz representation theorem
Every bounded functional on a Hilbert space is an inner product.