A note on homomorphisms of inner product spaces

• Autorzy: Pulmannova S.
• Języki publikacji: EN

Abstrakty

EN

Recently, Buhagiar and Chetcuti [1] have shown that if V1 and V2 are two separable, real inner product spaces such that the modular ortholattices of their finite and cofmite subspaces are algebraically isomorphic, then V1 and V2 are isomorphic as inner product spaces. Their proof is based on the properties of inner product spaces, in particular it makes use of Gleason's theorem. In this note we show, using techniques of projective geometry, that their result holds for any inner product spaces, real, complex or quaternionic, of dimension at least three, not necessarily separable. We also consider the case when the algebraic isomorphism is replaced by a homomorphism, and the case when the underlying fields of V1 and V2 are not the same.

Słowa kluczowe

EN

homomorphism; semilinear map; finite subspaces; projective geometry; orthogeometry; morphism

PL

homomorfizm; geometria projektywna; ortogeometria; odwzorowania

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 997--1004
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Pulmannova S.

• Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, SK-814 73 Bratislava, Slovakia

Bibliografia

• [1] D. Buhagiar, E. Chetcuti, On isomorphisms of inner product spaces, Math. Slovaca 54 (2004), 109-117.
• [2] A. Dvurečenskij, Gleason’s Theorem and Its Applications, Kluwer Acad. Publ./Ister Science Press, Dordrecht/Bratislava, 1992.
• [3] A. Dvurečenskij, A. Pullmanová, On the homomorphisms of sum logics, Ann. Inst. Henri Poincaré/Physique théoretique 54 (1991), 223-228.
• [4] C. A. Faure, A. Frölicher, Modern Projective Geometry, Kluwer Acad. Publ., Dordrecht, 2000.