Weeks | Topics |
1 |
Linear Operator, Kernel of a Linear Operator, Isomorphism
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2 |
Bounded and Continuous Linear Operators
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3 |
Bounded and Continuous Linear Operators
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4 |
Bounded Linear Extensions, Linear Functionals and Dual Space
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5 |
Algebraic Dual Space, Linear Operators and Functionals on Finite Dimensional Spaces
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6 |
Hahn-Banach Theorem, Hahn-Banach Theorem for Complex Linear Spaces and Normed Spaces, Baire Theorem
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7 |
Open Mapping Theorem, Closed Linear Operators and Closed Graph Theorem
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8 |
Banach-Steinhouse Theorem, Adjoint Operator for Normed Spaces
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9 |
Midterm Exam
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10 |
Inner Product Space, Parallelogram Equality, Orthogonality, Pythagorean Theorem
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11 |
Hilbert Space, Orthogonal Complement and Direct Sum
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12 |
Closed Subspace, Minimizing Vector Theorem, Orthogonal Projection Operator
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13 |
Riesz’s Theorem, Hilbert-adjoint Operator
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14 |
Self-Adjoint and Normal Operators
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