# Banach 23

The lecture: banach23

### Excerpts

Definitions

- External direct sums of Hilbert spaces
- Internal direct sums of Hilbert subspaces
- Unitary operator between Hilbert spaces

Results

- implies
- is algebra with taking adjoint as involution.
- for all implies . (in the pf its supposed to say , and are using sequilinear innerproduct .
- idempotent is orthogonal projection iff
- is self adjoint iff .
- is unitary iff it is invertible and isometric.
- is normal iff .

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## About this entry

You’re currently reading “Banach 23,” an entry on Math Meandering

- Published:
- October 19, 2009 / 10:18 am

- Category:
- Banach Algebras (Course)

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