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