On trivial and non-trivial n - Homogeneous C* algebras

Anatoly Antonevich; Naum Krupnik

doi:10.1007/BF01200122

On trivial and non-trivial n - Homogeneous C* algebras

Anatoly Antonevich, Naum Krupnik

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let A be a C*-algebra for which all irreducible representations are of dimensional n. Then ([F], [TT], [V]) algebra A is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle ε_A. The basis X of this bundle coincides with the compact of all maximal two-sided ideals of A. We obtain some conditions which provide that ε_A is trivial and this yields that A is isomorphic to the algebra of all n × n matrix functions continuous on X. In the case when X = Sⁿ is a sphere we describe the set of algebraic bundles over X and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested.

Original language	English
Pages (from-to)	172-189
Number of pages	18
Journal	Integral Equations and Operator Theory
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/BF01200122
State	Published - 2000

Bibliographical note

Funding Information:
belong to the center of B0 and separate the points of D/S 1. Indeed, if Zl, z2 E D, zl ~ z2 a nd bj(Zl)l--b.~(z~)l (y = 2, 3) then Iz~l--Iz21 and it follows from the equality #2(zl) = #2(z2) that \[zl\[= Iz21 = 1. But such points coincide in D/S x. Therefore the center separates the points of the space D/S 1 and, by Proposition 7.1, B0 = B. It follows from this example that Acknowledgments. The first author wishes to thank the Bar-Ilan University for the invitation and financial support. This work was also partially supported by the Fundamental Research Fund of the Republic of Belarus.

Funding

belong to the center of B0 and separate the points of D/S 1. Indeed, if Zl, z2 E D, zl ~ z2 a nd bj(Zl)l--b.~(z~)l (y = 2, 3) then Iz~l--Iz21 and it follows from the equality #2(zl) = #2(z2) that \[zl\[= Iz21 = 1. But such points coincide in D/S x. Therefore the center separates the points of the space D/S 1 and, by Proposition 7.1, B0 = B. It follows from this example that Acknowledgments. The first author wishes to thank the Bar-Ilan University for the invitation and financial support. This work was also partially supported by the Fundamental Research Fund of the Republic of Belarus.

Funders	Funder number
Fundamental Research Fund of the Republic of Belarus
Bar-Ilan University

Access to Document

10.1007/BF01200122

Cite this

@article{c5d8185f495342d79b63e7fa25c30d79,

title = "On trivial and non-trivial n - Homogeneous C* algebras",

abstract = "Let A be a C*-algebra for which all irreducible representations are of dimensional n. Then ([F], [TT], [V]) algebra A is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle εA. The basis X of this bundle coincides with the compact of all maximal two-sided ideals of A. We obtain some conditions which provide that εA is trivial and this yields that A is isomorphic to the algebra of all n × n matrix functions continuous on X. In the case when X = Sn is a sphere we describe the set of algebraic bundles over X and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested.",

author = "Anatoly Antonevich and Naum Krupnik",

note = "Funding Information: belong to the center of B0 and separate the points of D/S 1. Indeed, if Zl, z2 E D, zl ~ z2 a nd bj(Zl)l--b.~(z~)l (y = 2, 3) then Iz~l--Iz21 and it follows from the equality #2(zl) = #2(z2) that \[zl\[= Iz21 = 1. But such points coincide in D/S x. Therefore the center separates the points of the space D/S 1 and, by Proposition 7.1, B0 = B. It follows from this example that Acknowledgments. The first author wishes to thank the Bar-Ilan University for the invitation and financial support. This work was also partially supported by the Fundamental Research Fund of the Republic of Belarus.",

year = "2000",

doi = "10.1007/BF01200122",

language = "אנגלית",

volume = "38",

pages = "172--189",

journal = "Integral Equations and Operator Theory",

issn = "0378-620X",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

TY - JOUR

T1 - On trivial and non-trivial n - Homogeneous C* algebras

AU - Antonevich, Anatoly

AU - Krupnik, Naum

N1 - Funding Information: belong to the center of B0 and separate the points of D/S 1. Indeed, if Zl, z2 E D, zl ~ z2 a nd bj(Zl)l--b.~(z~)l (y = 2, 3) then Iz~l--Iz21 and it follows from the equality #2(zl) = #2(z2) that \[zl\[= Iz21 = 1. But such points coincide in D/S x. Therefore the center separates the points of the space D/S 1 and, by Proposition 7.1, B0 = B. It follows from this example that Acknowledgments. The first author wishes to thank the Bar-Ilan University for the invitation and financial support. This work was also partially supported by the Fundamental Research Fund of the Republic of Belarus.

PY - 2000

Y1 - 2000

N2 - Let A be a C*-algebra for which all irreducible representations are of dimensional n. Then ([F], [TT], [V]) algebra A is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle εA. The basis X of this bundle coincides with the compact of all maximal two-sided ideals of A. We obtain some conditions which provide that εA is trivial and this yields that A is isomorphic to the algebra of all n × n matrix functions continuous on X. In the case when X = Sn is a sphere we describe the set of algebraic bundles over X and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested.

AB - Let A be a C*-algebra for which all irreducible representations are of dimensional n. Then ([F], [TT], [V]) algebra A is isomorphic to algebra of all continuous sections of an appropriate algebraic bundle εA. The basis X of this bundle coincides with the compact of all maximal two-sided ideals of A. We obtain some conditions which provide that εA is trivial and this yields that A is isomorphic to the algebra of all n × n matrix functions continuous on X. In the case when X = Sn is a sphere we describe the set of algebraic bundles over X and algebraic structures on this set. Some applications to algebras generated by idempotents are suggested.

UR - http://www.scopus.com/inward/record.url?scp=0034355377&partnerID=8YFLogxK

U2 - 10.1007/BF01200122

DO - 10.1007/BF01200122

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0034355377

SN - 0378-620X

VL - 38

SP - 172

EP - 189

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

On trivial and non-trivial n - Homogeneous C* algebras

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this