C^*-algebras generated by scaling elements
Takeshi Katsura
TL;DR
This paper explores the structure of C^*-algebras generated by scaling elements, extending classical theorems and characterizing their projections.
Contribution
It generalizes the Wold decomposition and Coburn's theorem to scaling elements and characterizes when these algebras contain infinite projections.
Findings
Generalized classical theorems to scaling elements.
Provided criteria for the presence of infinite projections.
Enhanced understanding of the structure of these C^*-algebras.
Abstract
We investigate C^*-algebras generated by scaling elements. We generalize the Wold decomposition and Coburn's theorem on isometries to scaling elements. We also completely determine when the C^*-algebra generated by a scaling element contains an infinite projection.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Spectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods