Thesis (Selection of subject)

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Topological and descriptive methods in the theory of function and Banach spaces

Thesis title in Czech:	Topologické a deskriptivní metody v teorii funkčních a Banachový prostorů
Thesis title in English:	Topological and descriptive methods in the theory of function and Banach spaces
Key words:	Choquetova teorie, funkční prostor, simplex, abstraktní Dirichletův problém, slabě kompaktní operátor
English key words:	Choquet theory, function space, simplex, abstract Dirichlet problem, weakly compact operator
Academic year of topic announcement:	2007/2008
Thesis type:	dissertation
Thesis language:	angličtina
Department:	Department of Mathematical Analysis (32-KMA)
Supervisor:	prof. RNDr. Jiří Spurný, Ph.D., DSc.
Author:	hidden - assigned and confirmed by the Study Dept.
Date of registration:	07.11.2007
Date of assignment:	19.11.2007
Date and time of defence:	15.04.2011 12:00
Date of electronic submission:	10.02.2011
Date of submission of printed version:	10.02.2011
Date of proceeded defence:	15.04.2011
Opponents:	prof. RNDr. Ivan Netuka, DrSc.
	prof. RNDr. Ondřej Kalenda, Ph.D., DSc.

Guidelines

Student se zaměří na hlubší vlastnosti objektů v Choquetově teorii funkčních prostorů, zejména na součiny a limity prostorů, Dieudonného vlastnost a afinní obrazy konvexních množin.

References

Johnson, W. B., Lindenstrauss, J.: Handbook of the geometry of Banach spaces, Vol. I and II, North-Holland, Amsterdam, 2001
Asimow, L., Ellis, A. J.: Convexity theory and its applications in functional analysis. London Mathematical Society Monographs, 16. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980.

Preliminary scope of work

Student se zaměří na hlubší vlastnosti objektů v Choquetově teorii funkčních prostorů, zejména na součiny a limity prostorů, Dieudonného vlastnost a afinní obrazy konvexních množin.

Preliminary scope of work in English

The sudent will study deeper properties of objects in the Choquet theory of function spaces, in particular, products and limits of function spaces, the Dieudonné property and affine images of convex sets.