Lecture 11

24 Outubro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

Properties of compact linear operators (cont.)

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Lecture 10

21 Outubro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

Ascoli-Arzelà Theorem: statement without a proof. The Fredholm integral operators are compact in C([a,b]) with the norm of uniform convergence. The Fredholm integral operators are compact in L^2([a,b]): a proof omitting some details. Point spectrum for an operator T in L(E), E a normed space. Examples.

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TP 5

17 Outubro 2024, 11:00 • Maria Teresa Faria da Paz Pereira

Exercices about properties of adjoint and self-adjoint operators.

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Lecture 9

17 Outubro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

Properties of adjoint and self-adjoint operators (cont.). Compact linear operators between two normed spaces E,F: definitions and general properties. The space of compact linear operators is closed in L(E,F) if F is Banach.

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Lecture 8

14 Outubro 2024, 10:30 • Maria Teresa Faria da Paz Pereira

Adjoint of a bounded operator between Hilbert spaces: definition, properties and examples. Adjoint of Fredholm and Volterra integral operators.

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