Generating wandering subspaces for doubly commuting covariant representations

Harsh Trivedi; Shankar Veerabathiran

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Generating wandering subspaces for doubly commuting covariant representations

Harsh Trivedi, Shankar Veerabathiran

Operator Algebras · Submitted 10 Apr 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We obtain a Halmos-Richter-type wandering subspace theorem for covariant representations of C*-correspondences.

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arXiv ID1904.05122 (version 2)

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CitationHarsh Trivedi, Shankar Veerabathiran. "Generating wandering subspaces for doubly commuting covariant representations." arXiv:1904.05122 (2019). https://pith.science/paper/WJASJGK3

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We obtain a Halmos-Richter-type wandering subspace theorem for covariant representations of C*-correspondences. Further the notion of Cauchy dual and a version of Shimorin's Wold-type decomposition for covariant representations of C*-correspondences is explored and as an application a wandering subspace theorem for doubly commuting covariant representations is derived. Using this wandering subspace theorem generating wandering subspaces are characterized for covariant representations of product systems in terms of the doubly commutativity condition.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We obtain a Halmos-Richter-type wandering subspace theorem for covariant representations of C*-correspondences.	result 0.75	0.95	0.51	asserted 1.00
s1	Further the notion of Cauchy dual and a version of Shimorin's Wold-type decomposition for covariant representations of C*-correspondences is explored and as an application a wandering subspace theorem for doubly commuting covariant representations is derived.	contribution 0.83	0.91	0.28	asserted 1.00
s2	Using this wandering subspace theorem generating wandering subspaces are characterized for covariant representations of product systems in terms of the doubly commutativity condition.	result 0.82	0.91	0.33	asserted 1.00

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Original abstract

We obtain a Halmos-Richter-type wandering subspace theorem for covariant representations of C*-correspondences. Further the notion of Cauchy dual and a version of Shimorin's Wold-type decomposition for covariant representations of C*-correspondences is explored and as an application a wandering subspace theorem for doubly commuting covariant representations is derived. Using this wandering subspace theorem generating wandering subspaces are characterized for covariant representations of product systems in terms of the doubly commutativity condition.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as background 1 paper

In recent years, there has been several papers on the Wold decomposition in the multivariable Operator Theory, see [ref] .

Doubly commuting invariant subspaces for representations of product systems of $C^*$-correspondences · Introduction · 0.99

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