Displaying similar documents to “On contradictions of normed vector spaces”

Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.

Carlos Benítez Rodríguez (1989)

Revista Matemática de la Universidad Complutense de Madrid

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Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized...

On the non-existence of norms for some algebras of functions

Bertram Yood (1994)

Studia Mathematica

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Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for Ω = ℝ n where ℝ is the reals.

On (a,b,c,d)-orthogonality in normed linear spaces

C.-S. Lin (2005)

Colloquium Mathematicae

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We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.

On the lambda-property and computation of the lambda-function of some normed spaces.

Mohamed Akkouchi, Hassan Sadiky (1993)

Extracta Mathematicae

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R. M. Aron and R. H. Lohman introduced, in [1], the notion of lambda-property in a normed space and calculated the lambda-function for some classical normed spaces. In this paper we give some more general remarks on this lambda-property and compute the lambda-function of other normed spaces, namely: B(S,∑,X) and M(E).