Functional Analysis In Asymmetric Normed Spaces
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Functional Analysis In Asymmetric Normed Spaces
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Author : Stefan Cobzas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-30
Functional Analysis In Asymmetric Normed Spaces written by Stefan Cobzas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis – completeness, compactness and Baire category – which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text.
Functional Analysis In Normed Spaces
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Author : Leonid Vitalʹevich Kantorovich
language : en
Publisher:
Release Date : 1964
Functional Analysis In Normed Spaces written by Leonid Vitalʹevich Kantorovich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Functional analysis categories.
Metric And Normed Spaces
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Author : A. N. Kolmogorov
language : en
Publisher:
Release Date : 1957
Metric And Normed Spaces written by A. N. Kolmogorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Functional analysis categories.
Elements Of The Theory Of Functions And Functional Analysis 1 Metric And Normed Spaces
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Author : Andrej N. Kolmogorov
language : en
Publisher:
Release Date : 1963
Elements Of The Theory Of Functions And Functional Analysis 1 Metric And Normed Spaces written by Andrej N. Kolmogorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
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Author :
language : en
Publisher:
Release Date : 1957
written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with categories.
Elements Of The Theory Of Functions And Functional Analysis 1 Metric And Normed Spaces
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Author : Andrej N. Kolmogorov
language : en
Publisher:
Release Date : 1963
Elements Of The Theory Of Functions And Functional Analysis 1 Metric And Normed Spaces written by Andrej N. Kolmogorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Semitopological Vector Spaces
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Author : Mark Burgin
language : en
Publisher: CRC Press
Release Date : 2017-06-26
Semitopological Vector Spaces written by Mark Burgin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Mathematics categories.
This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.
Elements Of The Theory Of Functions And Functional Analysis
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Author : Andreĭ Nikolaevich Kolmogorov
language : en
Publisher:
Release Date : 1957
Elements Of The Theory Of Functions And Functional Analysis written by Andreĭ Nikolaevich Kolmogorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Functional analysis categories.
Elements Of The Theory Of Functions And Functional Analysis
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Author : Andreĭ Nikolaevich Kolmogorov
language : en
Publisher:
Release Date : 1957
Elements Of The Theory Of Functions And Functional Analysis written by Andreĭ Nikolaevich Kolmogorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Functional analysis categories.
General Topology
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Author : Tom Richmond
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-07-06
General Topology written by Tom Richmond and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-06 with Mathematics categories.
The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.