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Isometries on symmetric spaces associated with semi-finite von Neumann algebras
Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be consid...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2017
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| Summary: | Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces. |
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