Triangle Congruence Characterizations of Inner Product Spaces
β Scribed by Charles R. Diminnie; Edward Z. Andalafte; Raymond W. Freese
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 309 KB
- Volume
- 144
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
The linear operator Tin an inner product space ( X , [ . , a ] ) is called contractive (expansive, XI, resp.) for all x E X . Eigenvalues, in particular those in the unit disc, and the signatures of the corresponding eigenspaces were studied e.g. ## in [IKL], [AI], [B], where also references to e
We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on