Throughout this paper, assume that x is a nonarchimedean normed space and that y. Stochastic processes on nonarchimedean spaces with values in. Fixed points and approximately octic mappings in nonarchimedean 2normed spaces. Nonarchimedean analogs of markov quasimeasures and stochastic processes are investigated. The only multiplicative norms on them are jjr 1for 0 non archimedean banach spaces, mediterranean journal of mathematics 2019. The only multiplicative norms on them are jjr 1for 0 pdf 389 kb for subscribers only. Pdf functional inequalities in nonarchimedean banach spaces.
In this paper, we prove the generalized hyersulam stability of the additivequadraticcubicquartic functional equation 0. Stochastic processes on nonarchimedean banach spaces. Fixed points and the stability of an aqcqfunctional equation. Topological homeomorphisms of banach spaces over nonarchimedean. Hur stability of a generalized apollonius type quadratic functional equation in nonarchimedean banach spaces. We describe some classes of linear operators on banach spaces over nonarchimedean fields, which admit orthogonal spectral decompositions. The only multiplicative norms on them are jjr 1for 0 non archimedean valued. Nonarchimedean function spaces and the lebesgue dominated convergence theorem kakol, j. This book is focused on the theory of linear operators on nonarchimedean banach spaces. Nearly quadratic nderivations on nonarchimedean banach algebras. Contents preface 3 1 conventions on nonarchimedean. Nonarchimedean banach spaces with automorphism groups that are transitive on the unit sphere. In this subsection we recall some basic notations from 7, 8 such as non archimedean elds, non archimedean normed.
Cardinality and mackey topologies of nonarchimedean. In lectures i proceed to the next chapter, on lebesgue. Here are considered spaces of functions with values in banach spaces over nonarchimedean local fields, in particular, with values in the field. Main results throughout this section, we assume that g is an additive group and x is a banach nonarchimedean space. In section 3, using the fixed point method, we prove the generalized hyersulam stability of the additivequadraticcubicquartic functional equation in non archimedean banach spaces for an even case. Simultaneous automorphisms in the in the space of entire functions over nonarchimedean fields. Journal of inequalities and applications fixed points and approximately octic mappings in non archimedean 2normed spaces choonkil park 2 madjid eshaghi gordji 0 mohammad bagher ghaemi 1 hamid majani 1 0 department of mathematics, semnan university, p. Pdf closed linear operators between nonarchimedean banach. Nearly quadratic nderivations on nonarchimedean banach. The jensen functional equation in nonarchimedean normed.
We describe a subclass of the class of normal operators on banach spaces over nonarchimedean fields a. The invariant subspace problem for nonarchimedean banach spaces 605 in 9. This book focuses on the theory of linear operators on nonarchimedean banach spaces. Spectral integration and spectral theory for nonarchimedean. Topological homeomorphisms of banach spaces over non archimedean. Ulam stability of cubic and quartic functional equations in non archimedean spaces. N, n 3 in nonarchimedean banach spaces mathematics subject classi. Let ebe a free banach space with an orthogonal base ej. Non archimedean functional analysis download ebook pdf.
The topics treated in this book range from a basic introduction to nonarchimedean valued fields, free nonarchimedean banach spaces, bounded and unbounded linear operators in the nonarchimedean setting, to the spectral theory for some classes of linear operators. In the sequel we will use the following definitions. Nonarchimedean analytic spaces the hebrew university. Weak and strong c1compactness in nonarchimedean banach spaces. This item appears in the following collections faculty of science 27186. The non archimedean spectral theory and spectral integration is developed. Letk be a locally compact nonarchimedean nontrivially valued field. In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex banach space sends some non trivial closed subspace to itself. Banach spaces frechet spaces references an introduction to non archimedean functional analysis wiesla w sliwa university of poznan, poland workshop on non archimedean functional analysis, lie groups and dynamical systems, university of paderborn, germany, february 812, 2010 wiesla w sliwa non archimedean functional analysis. The nonarchimedean spectral theory and spectral integration is developed.
In this chapter we gather some basic facts about non archimedean banach spaces, with a special emphasis on the socalled padic hilbert space. If every cauchy sequence in x converges, then the non archimedean normed space x is called a non archimedean banach space. Several approaches to nonarchimedean geometry the basic properties of t n are summarized in the following result that is analogous to properties of polynomial rings over a. In this article we caleulate duals of well known nonarchimedean banach spaces and find the statement above true for them. Let k be a nonarchimedean valued eld and let e be a nonarchimedean. Bhargav bhatt april 23, 2017 university of michigan. Many variants of the problem have been solved, by restricting the class of bounded operators considered or by. A pseudovalued space is a nonarchimedean pseudonormed linear. The proofs of these properties are inspired by the local study of complexanalytic spaces via weierstrass preparation techniques to carry out induction on n. Nonarchimedean banach spaces with automorphism groups. This site is like a library, use search box in the widget to get ebook that you want. Throughout, f will denote either the real line r or the complex plane c. It is to some extent a sequel of the authors recent work on linear. On the stability of pexider functional equation in nonarchimedean spaces on the stability of.
Vspaces depart from the classical normed linear spaces 7, 36 in that the usual requirements on the. Throughout this paper, assume that is a nonarchimedean normed vector space and that is a nonarchimedean banach space. Lecture notes for a class on perfectoid spaces bhargav bhatt april 23, 2017. Nonarchimedean operator theory toka diagana springer. Fixed points and approximately octic mappings in non. They are used for the development of stochastic antiderivations. Functional inequalities in nonarchimedean banach spaces. A nonarchimedean gurari i banach space g over a nonarchimedean valued eld k is constructed, i. Fixed points and the stability of an aqcqfunctional equation in nonarchimedean normed spaces. Normed vector spaces over a spherically complete field. Ulam stability of cubic and quartic functional equations in nonarchimedean spaces. All vector spaces are assumed to be over the eld f. Throughout this paper, assume that is a non archimedean normed vector space and that is a non archimedean banach space. Closed linear operators between nonarchimedean banach spaces.
Books on analytic functions on banach spaces over a non. A nonarchimedean stone banach theorem article pdf available in proceedings of the american mathematical society 1002. Non archimedean analogs of markov quasimeasures and stochastic processes are investigated. Again the results here are wellknown and will serve as background for the operator theory developed in later chapters. The stability problem of functional equations originated from a question of ulam concerning the stability of group homomorphisms. The topics treated in this book range from a basic introduction to non archimedean valued fields, free non archimedean banach spaces, bounded and unbounded linear operators in the non archimedean. Fixed points and the stability of an aqcqfunctional. Note that the banach space e of countable type is re. Pdf in this work, we prove the generalized hyersulam stability of the following functional inequality. Weak and strong c1compactness in nonarchimedean banach.
Locally convex spaces over nonarchimedean valued fields nonarchimedean functional analysis, where alternative but equally valid number systems such as padic numbers are fundamental, is a fastgrowing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. Finally, we give some remarks and conclusions in section 4. The topics treated in this book range from a basic introduction to non archimedean valued fields, free non archimedean banach spaces, bounded and unbounded linear operators in the non archimedean setting, to the spectral theory for some classes of linear operators. Diarra received 22 january 2001 and in revised form 8 august 2001 banach algebras over arbitrary complete non archimedean. Box 35195363, semnan, iran 1 department of mathematics, iran university of science and technology, narmak, tehran, iran 2 research.
Pdf functional inequalities in nonarchimedean banach. Let k be a nonarchimedean valued eld and let e be a nonarchimedean banach space over k. Hahnbanach extension property for banach spaces over non. Throughout this paper, assume that x is a non archimedean normed space and that y. In section 3, using the fixed point method, we prove the generalized hyersulam stability of the additivequadraticcubicquartic functional equation in nonarchimedean banach spaces for an even case. In this subsection we recall some basic notations from 7, 8 such as nonarchimedean elds, nonarchimedean normed spaces and nonarchimedean banach spaces. Banach, spaces and the process of completion of a normed space to a banach space. On countable tightness and the lindelof property in non. Functional inequalities in nonarchimedean banach spaces yeol je cho a, choonkil park b. This paper provides an elementary introduction to vladimir berkovichs theory of analytic spaces over nonarchimedean elds, focussing on topological aspects. Also, the stability problems in nonarchimedean banach. Funtional analysis lecture notes for 18 mit mathematics.
Functional inequalities in non archimedean banach spaces. For a banach space overk containing a dense subspace with the hahnbanach extension property one of the following two mutually exclusive conditions holds. Department of applied mathematics, moscow state technical university mirea, av. Inthis paper, weprovethegeneralized hyersulam stability. A nonarchimedean stonebanach theorem article pdf available in proceedings of the american mathematical society 1002. Open access publications 51642 freely accessible full text publications. Additivecubic functional equations from additive groups. The invariant subspace problem for nonarchimedean banach spaces. On the space of entire functions of several variables of finite growth over nonarchimedean fields.
This book focuses on the theory of linear operators on non archimedean banach spaces. Equations in nonarchimedean intuitionistic fuzzy normed spaces syed abdul mohiuddine, abdullah alotaibi, and mustafa obaid. Berkovich department of mathematics, the weizmann institute of science p. Normed and banach spaces in this chapter we introduce the basic setting of functional analysis, in the form of normed spaces and bounded linear operators. Click download or read online button to get non archimedean functional analysis book now. V spaces depart from the classical normed linear spaces 7. If every cauchy sequence in x converges, then the nonarchimedean normed space x is called a nonarchimedean banach space. In this article we caleulate duals of well known non archimedean banach spaces and find the statement above true for them. Pdf generalized functional inequalities in nonarchimedean. Topological homeomorphisms of banach spaces over non. We also discuss realizations of bruhattits buildings in nonarchimedean groups and ag varieties.
We investigate the hyersulamrassias stability of the jensen functional equation in nonarchimedean normed spaces and study its asymptotic behavior in two directions. The dual of any banach space e over k is reflexive, provided that the cardinals of e and k are nonmeasurable. Hyersulam stability of functional inequalities with three. Dwork, on the rationality of the zeta function of an algebraic variety. Im looking for good textbooks on analytic functions on banach spaces over a non archimedean field. On some non archimedean normed linear spaces i by pierre robert introduction this paper is the first of a series to be published under the same title and numbered i, ii, in this work we study a non standard type of pseudonormed linear spaces, herein called v spaces. Reflexive nonarchimedean banach spaces sciencedirect. Nonarchimedean analytic spaces annette werner abstract.
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