Talk:Hilbert C*-module
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A first extension
[edit]I added the landmark example of a Hermitian vector bundle over a locally compact space. Also I made some minor changes to the introduction in the remarks concerning KK-theory and Morita equivalence. I might come back and add/change more, especially I want to add some stuff on operator algebras associated to C*-modules. Opinions please: is a discussion of Morita equivalence for C*-algebras appropriate in this article or should it be done in a separate one?
Note from the first contributor
[edit]I do not pretend that this article in any way covers all that could be said about the area, being a brief discussion of the history, an outline of the basic definitions, and the mention of a scant few examples and properties – it's slightly more than the Mathworld entry has, but not by a lot.
Then again, I only came to do this because I intended to revise a few things and thought it would be a useful exercise to make some refining edits to an existing article on the area, only to find that there wasn't one. It seemed an odd gap worth filling, so I filled it. Touch wood, a genuine expert might come along and make improvements.
It's been fun. --Sturm 15:39, 5 March 2008 (UTC)
Addition on adjointables and correspondences
[edit]I have made two fairly large additions. The first is a description of the adjointable and compact maps on a Hilbert module, and as essential material ought to be uncontroversial.
In the second I added the definition of a C*-correspondence, and outlined the tensor product and Toeplitz algebra constructions. I intended to extend the second to describe the Cuntz-Pimsner construction as well, but have deferred this for later. I'm not sure whether this material belongs in a dedicated C*-correspondence article or not; currently there probably isn't enough to warrant a separate article.
The Cuntz-Pimsner construction (and so by necessity the Toeplitz construction, as an intermediate step) sees widespread mention in the literature, and I thought it was high time it appeared on Wikipedia.
I also thought that the existence of a correspondence section might provide the impetus necessary to make another user add a description of Morita equivalence.
Please note: I am a novice editor, so feel free to rework the sections. Nepenthous (talk) 18:47, 18 September 2024 (UTC)