Locally convex spaces over non-Archimedean valued fields

Locally convex spaces over non-Archimedean valued fields by C. Perez-Garcia Download PDF EPUB FB2

LOCALLY CONVEX SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry.

This survey paper shows the state of the art on non-archimedean functional analysis, whose central body is the theory of locally convex spaces over complete non-archimedean valued fields.

This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest by: Get this from a library.

Locally convex spaces over non-Archimedean valued fields. [C Perez-Garcia; Wilhelmus Hendricus Schikhof] -- "Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure.

Get this from a library. Locally Convex Spaces over Non-Archimedean Valued Fields. [C Perez-Garcia; W H Schikhof] -- A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory.

This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research.4/5(1).

Description: Locally convex spaces over non-Archimedean valued fields book presentation of results in p-adic Banach spaces, spaces over fields with an infinite rank valuation, Frechet (and locally convex) spaces with Schauder bases, function spaces, p-adic harmonic analysis, and related areas.

It showcases research results in functional analysis over nonarchimedean valued complete fields. Find many great new & used options and get the best deals for Cambridge Studies in Advanced Mathematics: Locally Convex Spaces over Non-Archimedean Valued Fields by W.

Schikhof and C. Perez-Garcia (, Hardcover) at the best online prices at eBay. Free shipping for many products. Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication; Information for Libraries; Author Resources; Advertise with MAA; Meetings.

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Invited Addresses; Invited Paper. Ultrametrics and valuations 3 Then d is an ultrametric, called the trivial clearly induces the discrete topology. Notice that, for any a ∈ X and for any r ≥ 1, X = B(a,r).So X is a ball with infinitely many radii, and every point of X serves as a centre.

Below we will state several basic facts on ultrametric spaces. Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry.

This book is the first to provide a comprehensive treatment of non-Archimedean locally convex. Sequence spaces and summability over valued fields is a research book aimed at research scholars, graduate students and teachers with an interest in Summability Theory both Classical (Archimedean) and Ultrametric (non-Archimedean).

The book presents theory and methods in the chosen topic, spread over 8 chapters that seem to be important at. In this book, our focus will be on the non-archimedean valuation.

More specifically, we will work on free Banach spaces over non-archimedean valued fields and Operator theory on them. In this chapter we shall first develop the theory of valuation and then we shall give many examples to illustrate the : Toka Diagana, François Ramaroson.

quential spaces, F rechet spaces, spa ces of ”C.T.” type and p erfect spaces. In this work, we will study, in the non-archimedean (n.a)c a s e,f o ra locally K − convex space E the fi. Several properties of compactoid sets in non-archimedean locally convex spaces with a Schauder basis are proved in this paper.

As a consequence we der Cited by: 2. Locally convex topological vector spaces We can then characterize the class of locally convex t.v.s in terms of ab-sorbing absolutely convex neighbourhoods of the origin. Theorem If X is a l.c.

t.v.s. then there exists a basis B of neigh-bourhoods of the origin consisting of absorbing absolutely convex subsets Size: KB. Q&A for professional mathematicians. In the beginning of the 7th chapter of the book "Spectral theory and analytic geometry over non-Archimedean fields" by Vladimir Berkovich one can find the phrase " tensor product functor is exact on.

Our main goal of this research is to present the theory of points for relatively cyclic and relatively relatively noncyclic p-contractions in complete locally K -convex spaces by providing basic conditions to ensure the existence and uniqueness of fixed points and best proximity points of the relatively cyclic and relatively noncyclic p-contractions map in locally K -convex : Edraoui Mohamed, Aamri Mohamed, Lazaiz Samih.

INTRODUCTION Throughout K denotes a non-archimedean non-trivially valued field which is complete under the metric induced by the valuation |: K [0, oo). For fun- damentals of locally convex spaces over K we refer to [9], [6]. In this paper all locally convex spaces are over K and assumed to be Haus- by: Locally Convex Spaces over Non-Archimedean Valued Fields (Cambridge Studies in Advanced Mathematics) C.

Perez-Garcia、W. Schikhof / Cambridge University Press / / USD (目前无人评价). I propose to give a survey of the results of the study of linear topological spaces over non-archimedean valued fields.

Proofs of theorems will not be given. based on the theory of locally K-convex spaces is given by Van Tiel, Monna A.F. () Linear Topological Spaces over Non-Archimedean Valued Fields.

In: Springer T.A. (eds Cited by: 2.W. H. Schikhof: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books.For questions about topological vector spaces whose topology is locally convex, that is, there is a basis of neighborhoods of the origin which consists of convex open sets.

This tag has to be used with (topological-vector-spaces) and often with (functional-analysis).