Sumários
25 Outubro 2023, 11:00
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Maria Teresa Faria da Paz Pereira
Complements of the Theorem of Spectral Decomposition for compact self-adjoint operators.
23 Outubro 2023, 10:30
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Maria Teresa Faria da Paz Pereira
Point spectrum of compact self-adjoint operators: main properties. Theorem of spectral decomposition of a compact self-adjoint operator.
18 Outubro 2023, 11:30
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Maria Teresa Faria da Paz Pereira
Examples and resolution of exercises of Chapter I.
18 Outubro 2023, 11:00
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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]): main ideas for a proof.
Point spectrum for an operator T in L(E), E a normed space.
16 Outubro 2023, 10:30
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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. Examples of compact linear operators.