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Rosenthal's subsequence splitting lemma
Ondřej, Štěpán ; Spurný, Jiří (advisor) ; Pyrih, Pavel (referee)
The aim of the thesis is to give complete and thorough proofs of some well-known results from the measure theory. Oftentimes, arguments from functional analysis will be used to prove these results. For example, we will use an enhanced version of Schur's theorem to prove the Nikodym theorem and the Vitali-Hahn-Saks theorem. Then we will focus on the weak compactness in L1 and we will present a proof of the Biting Lemma and its corollary Rosenthal's subsequence splitting lemma. 1
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Banach limits
Mierva, Jáchym ; Spurný, Jiří (advisor) ; Vlasák, Václav (referee)
Banach limits Bachelor thesis abstract Jáchym Mierva Banach limit is a continuous linear functional on the Banach space of real bounded sequences, which naturally extends the limit - in particular, it is positive and translation invariant. In this thesis we construct Banach limits with some additional properties and subquently give examples of their use in several proofs from measure theory and functional analysis. Using the theory of Banach limits, the existence of Lebesgue measure and the Josefson-Nissenzweig theorem are proven, the former being an original work of the author. 1
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Spectrum of Cesaro operators
Maleček, Matyáš ; Spurný, Jiří (advisor) ; Johanis, Michal (referee)
Title: Spectrum of cesàro operators Author: Matyáš Maleček Department of Mathematical Analysis: Department of Mathematical Analysis Supervisor: prof. RNDr. Jiří Spurný, Ph.D., DSc., Department of Mathematical Analysis Abstract: This thesis focuses on finding the spectrum of cesàro operator on classic sequence spaces, namely c0, c, ℓ∞ and ℓp . Keywords: cèsaro operator spectrum classic sequence spaces
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Design of the laboratory task for attack on fingerprint authentication
Spurný, Jiří ; Vyoral, Josef (referee) ; Burda, Karel (advisor)
This thesis deal with personal fingerprint authentication and contains basic types of fingerprint readers included their principles of working. In this thesis are collected published attempts to this type of biometric authentication and in detail described way, how these attempts were realized . Realization of lab measurement is mentioned in practical part of thesis, is designed based on collected and evaluated information. Tendency for realization was to use materials and procedures which are available on market as well as computer technology. So no special equipment is needed for realization. Practical part describes in detail procedures for papillary lines capturing and their electronic processing. Described is also way to break through optical finger print sensor. For confirmation of procedure was made 12 artificial finger casts from Lukopren material. There casts were used to attempt on optical sensor Microsoft Fingerprint Reader with 100% success. Based on realized tests to produce artificial casts was proposed procedure for realization of laboratory measurement. This procedure is described in main part of this thesis. Proposed procedure has been confirmed in 90 minutes time limit, based on requirement to achieve time limit of school training session.
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Pension reform in the Czech Republic and its risks
Spurný, Jiří ; Krahulec, Jan (referee) ; Škapa, Stanislav (advisor)
The diploma thesis deals with the pension reform and the pension system in the Czech Republic. The paper explains fundamental terms in the field and explains their function. The main aim of the thesis is a definition and risk analysis of individual parts of the pension system. The secondary aim is guidance how to use each of the parts of the system.
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Vector-valued integral representation
Rondoš, Jakub ; Spurný, Jiří (advisor) ; Galego, Eloi Medina (referee) ; Cúth, Marek (referee)
The thesis consists of seven research papers. The first two papers study the properties of fragmented convex functions, mainly the so-called maximum principle. The first paper deals with convex functions defined on compact convex subsets of locally convex spaces, the second one with the abstract convex functions defined on general compact Hausdorff spaces. The next four papers present results in the spirit of the well-known Banach-Stone theorem in the area of subspaces of continuous functions. The first of those four papers deals with the spaces of affine continuous complex functions on compact convex sets. The second paper extends the results of the first one to the context of general subspaces of continuous functions defined on locally compact spaces. The other two papers further extend the previous results to the case of Banach space-valued and Banach lattice-valued functions, respectively. The last paper is devoted to the study of the Banach-Mazur distance between subspaces of vector-valued continuous functions that have scattered boundaries. 1
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Lipschitz free p-spaces
Raunig, Tomáš ; Cúth, Marek (advisor) ; Spurný, Jiří (referee)
This thesis deals with a class of p-Banach spaces known as Lipschitz free p-spaces, where 0 < p ≤ 1. In the first part we describe their construction in detail and give proofs of their basic properties. Using these properties we then characterize the spaces. In the second part we derive a formula, which can under certain circumstances be used to calculate the p-norm on these spaces, and describe an algorithm which calculates the p-norm on finite-dimensional Lipschitz free p-spaces. 1
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Noncommutative Choquet theory
Šišláková, Jana ; Spurný, Jiří (advisor) ; Hamhalter, Jan (referee)
- ABSTRACT - Noncommutative Choquet theory Let S be a linear subspace of a commutative C∗ -algebra C(X) that se- parates points of C(X) and contains identity. Then the closure of the Choquet boundary of the function system S is the Šilov boundary relati- ve to S. In the case of a noncommutative unital C∗ -algebra A, consider S a self-adjoint linear subspace of A that contains identity and generates A. Let us call S operator system. Then the noncommutative formulation of the stated assertion is that the intersection of all boundary representa- tions for S is the Šilov ideal for S. To that end it is sufficient to show that S has sufficiently many boundary representations. In the present work we make for the proof of that this holds for separable operator system.
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Composition operators on function spaces
Novotný, Matěj ; Spurný, Jiří (advisor) ; Kalenda, Ondřej (referee)
Univerzita Karlova Abstract of the bachelor thesis Composition operators on function spaces Matěj Novotný, Praha 2011 In the thesis we define what is an composition operator on the space of continuous or measurable functions of one complex variable so that we may proceed to study its properties depending on properties of the mapping the operator is induced by. We search for conditions under which the operator is continuous, compact and an isomorphism. We roughly estimate the spectrum of an operator defined on a space of continuous functions. 1
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Convergence of probability measures
Starý, Ladislav ; Spurný, Jiří (advisor) ; Kurka, Ondřej (referee)
In this thesis we define two most common types of convergence of probability measures and show relations between them. Using examples, we show that our result is sharp. After that, we discuss weak convergence of probability measures and convergence of random variables in distribution defined by weak convergence of probability distributions. Above all, we provide a survey among various types of convergence of random variables and relations among them.
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