CODE 61705 ACADEMIC YEAR 2017/2018 CREDITS 8 cfu anno 1 MATEMATICA 9011 (LM-40) - 8 cfu anno 2 MATEMATICA 9011 (LM-40) - SCIENTIFIC DISCIPLINARY SECTOR MAT/05 TEACHING LOCATION SEMESTER 1° Semester TEACHING MATERIALS AULAWEB 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 LAURA BURLANDO Ricevimento: 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. ADA ARUFFO Ricevimento: At the end of lectures or by appointment. Exam Board LAURA BURLANDO (President) ADA ARUFFO FRANCESCA ASTENGO LESSONS LESSONS START The class will start according to the academic calendar. Class schedule ELEMENTS OF ADVANCED ANALYSIS 2 EXAMS EXAM DESCRIPTION Written and oral tests. ASSESSMENT METHODS There will be both a written test and an oral one. Exam schedule Data appello Orario Luogo Degree type Note 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 FURTHER INFORMATION Prerequisite: IAS 1 Attendance: recommended.
