Volume : VII, Issue : III, March - 2017

ON THE RELATIONSHIP BETWEEN AN ORTHOGONAL AND A COMPLETE REDUCIBLE CONTINUOUS LINEAR REPRESENTATION

Diah Junia Eksi Palupi

Abstract :

 A continuous linear representation c is a homomorphism from a topological group G into GLc(V) of all continuous bijective transformations. Representation c  is called an orthogonal if on the topological vectorspace V there is a positive definite symmetric bilinear function f invariant under c. Futhermore, c is said to be completely reducible if every invariant subspace U of  V has an invariant complement W. We have every orthogonal representation is completely reducible. Especially for a continuous linear representation from a compact topological group.

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Article: Download PDF   DOI : 10.36106/ijar  

Cite This Article:

Diah Junia Eksi Palupi, ON THE RELATIONSHIP BETWEEN AN ORTHOGONAL AND A COMPLETE REDUCIBLE CONTINUOUS LINEAR REPRESENTATION, INDIAN JOURNAL OF APPLIED RESEARCH : Volume‾7 | Issue‾3 | March‾2017

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