| 1 |
Introuction |
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| 2 |
Banach algebras |
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| 3 |
modular ideals |
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| 4 |
quotient spaces |
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| 5 |
algebra homomorphisms |
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| 6 |
Spectrum of a Banach algebra |
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| 7 |
Spectrum of a Banach algebra 2 |
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| 8 |
Spectral radius |
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| 9 |
Gelfand theorem |
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| 10 |
Gelfand representation 1 |
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| 11 |
Gelfand representation 2 |
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| 12 |
Gelfand representation 3 |
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| 13 |
Compact operators 1 |
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| 14 |
Compact operators 2 |
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| 15 |
C*-algebra |
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| 16 |
elements of a C*-algebra |
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| 17 |
Some examples and theorems 1 |
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| 18 |
Some examples and theorems 2 |
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| 19 |
Polar decomposition |
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| 20 |
Spectral theorem 1 |
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| 21 |
Spectral theorem 2 |
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| 22 |
Spectral theorem 3 |
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| 23 |
Functional calculus 1 |
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| 24 |
Functional calculus 2 |
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| 25 |
Functional calculus 3 |
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| 26 |
positive elements |
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| 27 |
1 trace class operators |
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| 28 |
trace class operators 2 |
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| 29 |
Gelfand Naimark 1 |
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| 30 |
Gelfand Naimark 2 |
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| 31 |
Gelfand Naimark 3 |
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| 32 |
Von Neumann algebra 1 |
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| 33 |
Von Neumann algebra 2 |
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| 34 |
Von Neumann algebra 3 |
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