Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Analiză reală şi complexă (în limba engleză)
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MO266	Special Topics in Modern Mathematics (1)	

Semester	Hours: C+S+L	Category	Status	
1	2+1+0		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
Surname	title	title		C	S	L	
ANISIU Valeriu	Ph.D.	Assoc.Prof.	Function Theory	*	*		

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
Surname	title		position	C	S	L	

III. Course objectives
The goal of this course is to provide students rather deep knowledge modern Banach space theory. After completing the course, the student will have a solid understanding of mechanisms and tools used in this branch of Functional Analysis.	

IV. Course contents
1. Recall of the basic principles of Functional Analysis
2. Classical Banach spaces
3. Special properties and universality
4. Small sets	

V. Bibliography
1. M. FABIAN, P. HABALA et al.: Functional analysis and infinite dimensional geometry. Springer 2000
2. T. PRECUPANU: Spatii liniare topologice si elemente de analiza convexa. Ed. Academiei, Bucuresti 1992
3. G. SIRETCHI: Analiza functionala. Univ. Bucuresti 1982
4. G. SIRETCHI: Spatii concrete in analiza functionala. Univ. Bucuresti 1982
5. Y. BENYAMINI, J. LINDENSTRAUSS: Geometric nonlinear functional analysis. AMS 2000 
6. R.R. PHELPS: Convex Functions, Monotone Operators and Differentiability. 2nd edition. Lecture Notes in Mathematics No 1364. Springer-Verlag 1993.

VI. Thematic of didactic activities per weeks
1. Classical Banach Spaces
2. Adjoints, Projections, Quotients
3. Bases in Banach Spaces I
4. Bases in Banach Spaces II
5. Special Properties of c_0, 1_1, and  l_oo
6. Bases and Duality
7. L_p Spaces
8. Convexity
9. C(K) Spaces
10. Weak Compactness in L_1
11. The Dunford–Pettis Property
12. Structure of Banach spaces. Universality.
13. Porosity in Banach spaces.
14. Small sets.	

VII. Didactic methods used
Lectures, interactive presentations, exercises, individual study, homework assignments.	

VIII. Assessment
Projects (30%) and final test (70%). 	

IX. Additional references
1. C. Zalinescu - Convex Analysis in General Vector Spaces, World Scientific 2002
2. C. Bessaga, A. Pelczynski - Selected topics in infinite dimensional topology, 
3. J. Lindenstrauss, L. Tzafriri L. - Classical Banach spaces I, II, reprint, Springer, 1996
4. W. Rudin - Functional analysis – MGH 1973
5. E. Schechter - Handbook of Analysis and its Foundations. Academic Press 1999 (CD-ROM version)

	Dean,							Chair head,
       Prof. dr. Leon Ţâmbulea                         Prof. dr. Grigore Sălăgean

	Date,							Course responsible,
	March 3, 2009					Valeriu Anisiu