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The path space of a higher-rank graph

Samuel B. G. Webster (2011)

Studia Mathematica

We construct a locally compact Hausdorff topology on the path space of a finitely aligned k-graph Λ. We identify the boundary-path space ∂Λ as the spectrum of a commutative C*-subalgebra D Λ of C*(Λ). Then, using a construction similar to that of Farthing, we construct a finitely aligned k-graph Λ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ∂Λ̃. We show that when Λ is row-finite, we can identify C*(Λ) with a full corner of C*(Λ̃), and deduce that D Λ is isomorphic...

The strong Morita equivalence for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras

Kazunori Kodaka, Tamotsu Teruya (2015)

Studia Mathematica

Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional C*-Hopf algebra on a Hilbert C*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras.

The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

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