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
Domains of Analyticity in Real Normed Spaces
β Scribed by J. Schmets; M. Valdivia
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 374 KB
- Volume
- 176
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Probabilistic normed spaces have been redefined by Alsina, Schweizer, and Sklar. We give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity.
Let β¦1, β¦2 be open subsets of R d 1 and R d 2 , respectively, and let A(β¦1) denote the space of real analytic functions on β¦1. We prove a Glaeser type theorem by characterizing when a composition operator CΟ : Using this result we characterize when A(β¦1) can be embedded topologically into A(β¦2) as
It is shown that if a separable real Banach space X admits a separating analytic Ε½ Ε½ . function with an additional condition property K , concerning uniform behaviour . of radii of convergence then every uniformly continuous mapping on X into any real Banach space Y can be approximated by analytic o
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