Here, the underlying field K of any vector space shall be either \mathbb{R} or \mathbb{C} . Moreover, subspace will always denote the subspace of a vector space. Definition 1 A seminorm on a vector …
:being a mathematical entity upon which a norm is defined anormedvector space Word History First Known Use 1935, in the meaning definedabove Time Traveler The first known use ofnormedwas in 1935 See more words from the same year Dictionary Entries Nearnormed ...
For the analysis of vector spaces, it is important to impose more structure on the space than merely the algebraic conditions in Definition 1.2.1. The purpose of this chapter is to consider norms on vector spaces and some of their properties. The key concept of a norm is presented in ...
Define normed. normed synonyms, normed pronunciation, normed translation, English dictionary definition of normed. n. 1. a. A pattern that is regarded as typical of something: a neighborhood where families with two wage-earners are the norm. b. A standar
Definition 1 (Normed space)LetXbe avector spaceover thefieldK=CorR. A mapN:X→Ris called a norm onX, and(X,N)is anormed space, if: N0.N(u)≥0for anyu∈X, N1.N(λu)=|λ|N(u)for anyλ∈Kandu∈X, N2.N(u+v)≤N(u)+N(v), for anyu,v∈X, ...
1 Vector,metric,normedandBanachspaces1.1 VectorspacesWithFwewilldenotethefieldofrealnumbersRorthefieldofcomplexnumbersC.Definition1.1.Avectorspace(alsocalledalinearspace)overthefieldFisasetEwithtwooperations:1.Addition:TakesanytwoelementsxandyandassignsforthemathirdelementofE,whichiscompletelywrittenasx+yandwhich...
In this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced; and the boundedness ... JZ Xiao,XH Zhu - Elsevier North-Holland, Inc. 被引量: 206发表: 2003年 Hyperspaces of Normed Linear Spaces with the Attouch–Wets...
Such a function is usually designated by , anormof the vector . The existence of such a norm gives rise to the following definition: A linear space equipped with a norm is called anormed linear space. Example 1:Every inner product of an inner product space determines the norm given by whi...
In this paper we consider general t-norm in the definition of fuzzy normed linear space which is introduced by the authors in an earlier paper. It is prove... T Bag,SK Samanta - 《J Fuzzy Math》 被引量: 604发表: 2003年 On the intuitionistic fuzzy topological spaces In this paper, we...
The aim of this article is to extend results of Maslyuchenko, Mykhaylyuk and Popov about narrow operators on vector lattices. We give a new definition of a... M Pliev - 《Central European Journal of Mathematics》 被引量: 18发表: 2011年 Classical analysis on normed spaces 2nd Edition Ava...