ELEMENTS OF ADVANCED ANALYSIS 2

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Code
61705
ACADEMIC YEAR
2017/2018
CREDITS
8 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/05
TEACHING LOCATION
GENOVA (Mathematics)
semester
1° Semester
Teaching materials

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.

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