| 1 |
Operators on Banach Spaces |
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| 2 |
Compact Operators |
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| 3 |
Weakly Compact Operators |
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| 4 |
Operators on Hilbert spaces |
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| 5 |
Banach Algebras |
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| 6 |
Group of the Invertible Elements |
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| 7 |
Commutative Banach Algebras |
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| 8 |
Gelfand Map |
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| 9 |
off |
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| 10 |
C*-Algebras |
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| 11 |
Continuous Functional Calculus |
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| 12 |
Commutative C*-Algebras |
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| 13 |
Gelfand-Naimark Theorem (Commutative Case) |
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| 14 |
Some Examples of C*-Algebras |
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| 15 |
Positive Elements |
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| 16 |
Midterm Exam. |
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| 17 |
Positive Functional |
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| 18 |
States |
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| 19 |
Gelfand-Naimark-Segal Construction |
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| 20 |
Gelfand-Naimark Theorem (General Case) |
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| 21 |
Some Applications |
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| 22 |
Some Topologies on B(H) |
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| 23 |
Kaplansky Density Theorem |
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| 24 |
von Neumann Algebras |
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| 25 |
Bicommutatnt Theorem |
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| 26 |
Commutative von Neumann Algebras |
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| 27 |
Predual of B(H) |
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| 28 |
Predual of L^1(H) |
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| 29 |
W^*-Algebras and Sakai Theorem |
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| 30 |
Some Applications |
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| 31 |
Representation of C*-Algebras |
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| 32 |
Some Exercies |
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| 33 |
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