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.
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.
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: the contents of the courses "AF 1" and "AF2".
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.
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.
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
Ricevimento: At the end of lectures or by appointment.
LAURA BURLANDO (President)
ADA ARUFFO
The class will start according to the academic calendar.
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.
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.
Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teacher about the course.
