Representations of Starshaped Sets in Normed Linear Spaces
β Scribed by J. Cel
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 132 KB
- Volume
- 174
- Category
- Article
- ISSN
- 0022-1236
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π SIMILAR VOLUMES
## Abstract A triple (__x, y, z__) in a linear 2βnormed space (__X__, β.,.β) is called an __isosceles orthogonal triple__, denoted |(__x, y, z__), if |(.,.,.) is said to be __homogeneous__ if |(__x, y, z__) implies |(__ax, y, z__) for all real __a__ and it is __additive__ if |(__x~1~__, __y, z__)
The concept of orthogonality in normed linear spaces has been studied extensively by BIRKHOFF [3], JAMES IS], [7], [8], and the present authors [l], 151, among others. The most natural notion of orthogonality arises in the case where there is an inner product (-, -) compatible with the norm 11. 11 o
A number of writers have defined a concept of angle in a normed linear space or metric space by means of the law of cosines, and have studied the properties of these angles obtaining, in some cases, characterizations of real inner product spaces. (For a summary of earlier results see MARTIN and VAL