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Semicrossed Products of Operator Algebras by Semigroups.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2017Copyright date: ©2016Edition: 1st edDescription: 1 online resource (110 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470436971
Subject(s): Genre/Form: Additional physical formats: Print version:: Semicrossed Products of Operator Algebras by SemigroupsDDC classification:
  • 512.55600000000004
LOC classification:
  • QA326.D385 2017
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Operator algebras -- 2.2. Semigroups -- 2.3. Completely positive definite functions of groups -- 2.4. Completely positive definite functions of semigroups -- 2.5. Lattice-ordered abelian groups -- Chapter 3. Semicrossed products by abelian semigroups -- 3.1. Defining semicrossed products by abelian semigroups -- 3.2. The unitary semicrossed product -- 3.3. The isometric semicrossed product -- 3.4. The contractive semicrossed product by \bZ₊² -- 3.5. The Fock algebra -- Chapter 4. Nica-covariant semicrosssed products -- 4.1. The regular contractive semicrossed product -- 4.2. The Nica-covariant semicrossed product -- 4.3. The Nica-covariant semicrossed product by \bZⁿ₊ -- 4.4. Minimality and ideal structure -- 4.5. Comparison with C*-correspondences and product systems -- Chapter 5. Semicrossed products by non-abelian semigroups -- 5.1. Possible extensions to non-abelian semigroups -- 5.2. The semicrossed product by an Ore semigroup -- 5.3. The semicrossed product by \bF₊ⁿ -- Bibliography -- Back Cover.
Summary: The authors examine the semicrossed products of a semigroup action by *-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.
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Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Operator algebras -- 2.2. Semigroups -- 2.3. Completely positive definite functions of groups -- 2.4. Completely positive definite functions of semigroups -- 2.5. Lattice-ordered abelian groups -- Chapter 3. Semicrossed products by abelian semigroups -- 3.1. Defining semicrossed products by abelian semigroups -- 3.2. The unitary semicrossed product -- 3.3. The isometric semicrossed product -- 3.4. The contractive semicrossed product by \bZ₊² -- 3.5. The Fock algebra -- Chapter 4. Nica-covariant semicrosssed products -- 4.1. The regular contractive semicrossed product -- 4.2. The Nica-covariant semicrossed product -- 4.3. The Nica-covariant semicrossed product by \bZⁿ₊ -- 4.4. Minimality and ideal structure -- 4.5. Comparison with C*-correspondences and product systems -- Chapter 5. Semicrossed products by non-abelian semigroups -- 5.1. Possible extensions to non-abelian semigroups -- 5.2. The semicrossed product by an Ore semigroup -- 5.3. The semicrossed product by \bF₊ⁿ -- Bibliography -- Back Cover.

The authors examine the semicrossed products of a semigroup action by *-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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