|
|
Topological and descriptive methods in the theory of function and Banach spaces
Kačena, Miroslav
The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.
|
|
|
Integral operators on function spaces
Peša, Dalimil ; Pick, Luboš (advisor) ; Nekvinda, Aleš (referee)
In this thesis, we consider Lorentz-Karamata spaces with slowly varying fuc- tions and study their properties. We first provide simpler definition of slowly varying functions and derive some of their properties. We then consider Lorentz-Karamata functionals over an arbi- trary sigma-finite measure space equipped with a non-atomic measure and corre- sponding Lorentz-Karamata spaces. We characterise non-triviality of said spaces, then study when they are equivalent to a Banach function space and obtain mul- titude of conditions, either sufficient or necessary. We further study embeddings between Lorentz-Karamata spaces and provide a partial characterisation. At last, we try to describe the associate spaces of Lorentz-Karamata spaces and succeed even in some of the limiting cases. Our contribution is mainly the characterisation of non-triviality, the partial characterisation of embeddings, the description of associate spaces in some lim- iting cases and all the results concerning Lorentz-Karamata spaces with the sec- ondary parameter q smaller than one. Those results are, as far as we are aware, new. 1
|
|
|
Topological and descriptive methods in the theory of function and Banach spaces
Kačena, Miroslav
The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.
|
|
|
Topological and descriptive methods in the theory of function and Banach spaces
Kačena, Miroslav ; Spurný, Jiří (advisor) ; Netuka, Ivan (referee) ; Kalenda, Ondřej (referee)
The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.
|
|
|
Nelineární analýza, prostory funkcí a aplikace, Roč. 8
Rákosník, Jiří
The proceedings contain five invited lectures presented at the Spring School organized by the Institute of Mathematics AS CR in collaboration with the Czech University of Agriculture at Prague. The series of the spring schools has been organized in four years period since 1978 with the aim to bring together a broad audience including experienced mathematicians as well as students and to offer them extensive surveys of recent developments in the named fields delivered by distinguished specialists. All published papers were subject to the standard referee procedure.
|
|
|
Prostory funkcí, diferenciální operátory a nelineární analýza
Drábek, P. ; Rákosník, Jiří
The proceedings contain four of the invited main lectures and 23 selected contributions by the participants. All published papers were subject to the standard referee procedure. The conference was the sixth in the series of international meetings organized under the same name alternatively in Finland, Germany and Czech Republic since 1988. This conference was devoted to the seventieth birthday of Prof. Alois Kufner, the founder of the Czech school on the theory of function spaces.
|
guest ::
