Before Memmo my notes were scattered across PDFs. Now a workspace pulls everything into one place — I see exactly what's still left to study.
This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.
Before Memmo my notes were scattered across PDFs. Now a workspace pulls everything into one place — I see exactly what's still left to study.
Memmo's summaries are gold before exams. I don't have to re-read 800 pages two weeks before — just the important parts.
The AI chat has saved me the night before an exam more than once. I just keep asking until I get it — no waiting on a study group to reply.
The quizzes hit exactly what I need to know. Memmo tracks what I get stuck on — so I only practice what's worth it.
Flashcards with spaced repetition are magic. Memmo knows when I'm about to forget something and brings it back.
The AI podcasts are my favorite. I listen on my way to school and get a recap without sitting at a computer.
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