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.
Keywords :
Topological group bilinear function orthogonal and completely reducible continuous linear representation
Article:
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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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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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