OVERVIEW

This course deals with impotant topics in Functional Analysis and Operator Theory, which complete and develop the contents of the courses "Analisi Funzionale 1" and "Analisi Funzionale 2".

The lectures are delivered in Italian.

AIMS AND CONTENT

LEARNING OUTCOMES

To provide some advanced 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.

AIMS AND LEARNING OUTCOMES

This course provides some advancedl contents in Functional Analysis and Operator Theory. Students are expected to understand the concepts and the proofs that have been shown in the classes. In particular, they are expected to be able to provide proofs consisting in simple variants of the proofs that have been shown in the classes, to construct examples and to solve exercises about the topics developed in the course.

PREREQUISITES

Prerequisites: the contents of the courses "AF 1" and "AF2".

TEACHING METHODS

Teaching style: lectures (52 hours), given in the mode that will be decided by the University of Genova. Some of the lectures will be devoted to exercises.

SYLLABUS/CONTENT

Banach algebras; C^*-algebras; the specral theorem for normal operators on a Hilbert space; holomorphic functional calculus and the spectral mapping theorem; further elements of operator theory: study of isolated points of the spectrum, Fredholm operators.

RECOMMENDED READING/BIBLIOGRAPHY

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

C. E. Rickart, General Theory of Banach Algebras

S. R. Caradus, W.E. Pfaffenberger, B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces

TEACHERS AND EXAM BOARD

Exam Board

LAURA BURLANDO (President)

ADA ARUFFO

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written and oral tests. The written test consists of exercises concerning the contents of the syllabus. During the written test, students are allowed to consult the notes they have taken in the classes, as well as textbooks, only in paper form. The oral test can be taken whichever grade the student has got in the written test, and must be taken in the same round of the written test.

ASSESSMENT METHODS

There will be both a written test and an oral one. Each of them is intended to verify understanding by the student of the concepts and of the proofs developed in the classes, as well as ability in producing proofs consisting of simple variants of the proofs that have been shown in the classes, in constructing examples and in solving exercises concerning the syllabus.

Exam schedule

FURTHER INFORMATION

Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teacher about the course.