Linear algebra and differential geometry on abstract Hilbert space

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Linear algebra and differential geometry on abstract Hilbert space

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. ...

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Coordinate formalism on abstract Hilbert space

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Real-linear Operators on Quaternionic Hilbert Space

The main result is that any continuous real-linear operator A on a quaternionic Hubert space has a unique decomposition A=A0+iiAl + izAi+iiA3, where the A„ are continuous linear operators and (fi,f2,'3) is any right-handed orthonormal triad of vector quaternions. Other results concern the place of the colinear and complex-linear operators in this characterisation and the effect on the Av of a r...

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ژورنال

عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences

سال: 2005

ISSN: 0161-1712,1687-0425

DOI: 10.1155/ijmms.2005.2241