Abstract
A new constant mathit{WD}(X) is introduced into any real 2^{n}-dimensional symmetric normed space X. By virtue of this constant, an upper bound of the geometric constant D(X), which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrary m-dimensional symmetric normed linear space (mgeq2). As an application, the result is used to prove a special case for the reverse Hölder inequality.
Highlights
1 Introduction The notion of orthogonality has many forms when the underlying space is transferred from inner product spaces to real normed spaces
As we discuss in Corollary, this bound can be extended to any m-dimensional symmetric normed linear space (m ≥ )
In order to present an upper bound of D(X), a new constant WD(X) for any real normed linear space X = (R n, · ) is introduced
Summary
The notion of orthogonality has many forms when the underlying space is transferred from inner product spaces to real normed spaces. Birkhoff [ ] introduced Birkhoff orthogonality in which X is assumed to be a real normed linear space. These two types of orthogonality are different in general linear normed spaces. By considering the constant D(X) in n-dimensional real symmetric normed linear spaces, we obtain an upper bound WD(X).
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