CODE 61705 ACADEMIC YEAR 2016/2017 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. They can be given in English under request. 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 (besides the office hours communicated at the beginning of the course). Students are suggested to enroll in AulaWeb, in order to be able to get further information 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 GIANFRANCO BOTTARO LESSONS LESSONS START September 26, 2016 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 22/06/2017 10:00 GENOVA Scritto 21/07/2017 10:00 GENOVA Scritto 12/09/2017 10:00 GENOVA Scritto FURTHER INFORMATION Prerequisite: IAS 1 Attendance: recommended.
