## OVERVIEW

The lectures are delivered in Italian.

## AIMS AND CONTENT

LEARNING OUTCOMES

To provide some fundamental contents in Functional Analysis and Operator Theory that are considered important for the students who want to follow a PhD, or anyway aim to get a well grounded knowledge in the basic branches of Mathematics.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

Quotient normed spaces; reflexivity; weak topologies; compactness in spaces of continuous functions: the Ascoli-Arzelà theorem; elements of operator theory: spectrum, adjoint operator, compact operators, the spectral theorem for compact selfadjoint operators, unbounded operators, closed operators; elements of spectral theory in Banach algebras; Gelfand theory for commutative Banach algebras; introduction to C*-algebras; the Gelfand representation theorem for commutative C*-algebras.

RECOMMENDED READING/BIBLIOGRAPHY

A. E. Taylor, D. C. Lay: Introduction to Functional Analysis, 2nd edition

W. Rudin: Real and Complex Analysis

W. Rudin: Functional Analysis

## TEACHERS AND EXAM BOARD

**Office hours:** At the end of lectures or by appointment. Students are suggested to enroll in AulaWeb, in order to be able to get information and news by the teachers about the course.

**Office hours:** At the end of lectures or by appointment.

Exam Board

LAURA BURLANDO (President)

ADA ARUFFO

FRANCESCA ASTENGO

## LESSONS

TEACHING METHODS

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

Class schedule

## EXAMS

EXAM DESCRIPTION

Written and oral tests.

ASSESSMENT METHODS

There will be both a written test and an oral one.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

26/01/2018 | 10:00 | GENOVA | Scritto | |

16/02/2018 | 10:00 | GENOVA | Scritto | |

22/06/2018 | 10:00 | GENOVA | Scritto | |

20/07/2018 | 10:00 | GENOVA | Scritto | |

14/09/2018 | 10:00 | GENOVA | Scritto |