Pure states on 𝒪d

Ola Bratteli; Palle E. T Jorgensen; Akitaka Kishimoto; Reinhard F Werner

Back

Journal article

Pure states on 𝒪d

Ola Bratteli, Palle E. T Jorgensen, Akitaka Kishimoto and Reinhard F Werner

Journal of operator theory, Vol.43(1), pp.97-143

01/01/1997

View Online

Abstract

We study representations of the Cuntz algebras 𝓞d and their associated decompositions. In the case that these representations are irreducible, their restrictions to the gauge-invariant subalgebra UHFd have an interesting cyclic structure. If Si, 1 ≤ i ≤ d, are representatives of the Cuntz relations on a Hilbert space 𝓗, special attention is given to the subspaces which are invariant under ${\mathrm{S}}_{\mathrm{i}}^{*}$. The applications include wavelet multiresolutions corresponding to wavelets of compact support (to appear in the later paper [8]), and finitely correlated states on one-dimensional quantum spin chains.

Cuntz algebra

representations of C* -algebra

Hilbert space

endomorphism

completely positive maps

dilation

commutant

von Neumann algebras

Details

Title: Subtitle: Pure states on 𝒪d
Creators: Ola Bratteli
Palle E. T Jorgensen
Akitaka Kishimoto
Reinhard F Werner
Resource Type: Journal article
Publication Details: Journal of operator theory, Vol.43(1), pp.97-143
Publisher: Matematisk Institutt, Universitetet i Oslo
ISSN: 0379-4024
eISSN: 1841-7744
Language: English
Date published: 01/01/1997
Academic Unit: Mathematics
Record Identifier: 9984240863102771

Metrics

2 Record Views