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  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2021--22--A term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Basic Concepts in Modern Analysis

  \item[Course Number]
    \LRE{201‭.2‭.0351}

  \item[Course web page]\mbox{}\\
    \url{https://math.bgu.ac.il//en/teaching/fall2022/courses/basic-concepts-in-modern-analysis}

  \item[Lecturer]
    Prof. Victor Vinnikov,
    \nolinkurl{<vinnikov@bgu.ac.il>},
    Office 103

\item[Office Hours]
  \url{https://math.bgu.ac.il/en/teaching/hours}
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\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

Banach spaces and Hilbert spaces. Basic properties of Hilbert spaces. Topological vector spaces. Banach-Steinhaus theorem; open mapping theorem and closed graph theorem. Hahn-Banach theorem. Duality. Measures on locally compact spaces; the dual of $C(X)$. Weak and weak-$*$ topologies; Banach-Alaoglu theorem. Convexity and the Krein-Milman theorem. The Stone-Weierstrass theorem. Compact operators on Hilbert space. Introduction to Banach algebras and Gelfand theory. Additional topics as time permits.

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