Isomorphisms between topological conjugacy algebras
By K. Davidson, Elias G. Katsoulis. 2006
54 citations recorded by the source corpus.
Abstract A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that is a continuous proper map on a locally compact Hausdorff space , for i= 1,2. We show that the dynamical systems and are conjugate if and only if some topological conjugacy algebra of is isomorphic as an algebra to some topological conjugacy algebra of . This implies as a corollary the complete classification of the semicrossed products , which was previously considered by Arveson and Josephson [W. Arveson, K. Josephson, Operator algebras and measure preserving automorphisms II, J. Funct. Anal. 4 (1969), 100–134.], Peters [J. Peters, Semicrossed products of C*-algebras, J. Funct. Anal. 59 (1984), 498–534.], Hadwin and Hoover [D. Hadwin, T. Hoover, Operator algebras and the conjugacy of transformations, J. Funct. Anal. 77 (1988), 112–122.] and Power [S. Power, Classification of analytic crossed product algebras, Bull. London Math. Soc. 24 (1992), 368–372.]. We also obtain a complete classification of all semicrossed products of the form , where denotes the disc algebra and a continuous map which is analytic on the interior. In this case, a surprising dichotomy appears in the classification scheme, which depends on the fixed point set of η. We also classify more general semicrossed products of uniform algebras.
Subfields: Algebra and Number Theory, Materials Chemistry, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2aebad3674a3941f0e730f8a1e8b9136969ac359
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In Algebra and Number Theory
- Orr Shalit
- Adam H. Fuller
- E. Kakariadis
- K. Davidson
- B. Solel
- Gelu Popescu
- Michael Hartz
- E. Shamovich
In Materials Chemistry
In Mathematical Physics
- K. Davidson
- Orr Shalit
- Adam H. Fuller
- E. Kakariadis
- B. Solel
- Gelu Popescu
- Michael Hartz
- E. Shamovich
Citations in the corpus
- Subproduct systems (2009, methodology): “Elias Katsoulis has pointed out to us that the above corollary also follows from the techniques of [17].”
- Operator Algebras for Multivariable Dynamics (2007, unknown): “CHAPTER 2 Dilation Theory”
- Semicrossed Products of Operator Algebras by Semigroups (2014, background): “Recent progress [29, 30, 32, 61] shows that nonselfadjoint operator algebras form a sharp invariant for classifying systems and recovering the dynamics.”