Cohomology groups of a new class of Kadison-Singer algebras

An, Guangyu; Cheng, Xing; Sheng, Jun

doi:10.1007/s11425-022-2107-y

Sci. China Math.

2023

DOI: 10.1007/s11425-022-2107-y

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Cohomology groups of a new class of Kadison-Singer algebras

Guangyu An,

Xing Cheng,

Jun Sheng

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Cited by 2 publications

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Isomorphism of some new Kadison–Singer algebras

Yan,

Yang,

Yuan

et al. 2024

Banach J. Math. Anal.

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Isomorphism of some new Kadison–Singer algebras

Yan,

Yang,

Yuan

et al. 2024

Banach J. Math. Anal.

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The structure of Kadison-Singer lattices and the construction of strong Kadison-Singer algebras

Guangyu,

Danni,

Xing

et al. 2023

Sci. Sin.-Math.

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In this paper, we study the structure of Kadison-Singer lattices and strong Kadison-Singer algebras. We prove that every finite Kadison-Singer lattice on a finite-dimensional Hilbert space has no nontrivial reducing projections and construct a class of strong Kadison-Singer algebras on n-fold direct sums of infinite-dimensional separable Hilbert spaces. As a corollary, we show that there exist two Kadison-Singer algebras, such that their skew product is a strong Kadison-Singer algebra.

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Cohomology groups of a new class of Kadison-Singer algebras

Cited by 2 publications

References 14 publications

Isomorphism of some new Kadison–Singer algebras

Isomorphism of some new Kadison–Singer algebras

The structure of Kadison-Singer lattices and the construction of strong Kadison-Singer algebras

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