Elementary operators on Calkin algebras
This paper is dedicated to the memory of Professor Klaus Vala. Properties of elementary operators, especially on algebras of operators, have been vigorously studied over the past decades. It emerges that the situation of the Calkin algebra is full of surprises. In this setting, an elementary operato...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.595.9135 2023-05-15T18:41:22+02:00 Elementary operators on Calkin algebras Martin Mathieu The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.595.9135 http://www.maths.tcd.ie/pub/ims/bull46/S4602.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.595.9135 http://www.maths.tcd.ie/pub/ims/bull46/S4602.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://www.maths.tcd.ie/pub/ims/bull46/S4602.pdf text ftciteseerx 2016-01-08T13:44:08Z This paper is dedicated to the memory of Professor Klaus Vala. Properties of elementary operators, especially on algebras of operators, have been vigorously studied over the past decades. It emerges that the situation of the Calkin algebra is full of surprises. In this setting, an elementary operator with dense range is surjective, and injectiv-ity entails boundedness below. In the case of Hilbert space, positivity implies complete positivity, and the norm and the cb-norm of every el-ementary operator coincide. We present an overview on some results of this flavour, in particular on recent extensions of the latter two results to antiliminal-by-abelian C*-algebras (obtained by Archbold, Somerset, and the author), and strong rigidity properties of the norm of elemen-tary operators on Calkin algebras due to Saksman and Tylli. 1. Text tylli Unknown Klaus ENVELOPE(24.117,24.117,65.717,65.717) |
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This paper is dedicated to the memory of Professor Klaus Vala. Properties of elementary operators, especially on algebras of operators, have been vigorously studied over the past decades. It emerges that the situation of the Calkin algebra is full of surprises. In this setting, an elementary operator with dense range is surjective, and injectiv-ity entails boundedness below. In the case of Hilbert space, positivity implies complete positivity, and the norm and the cb-norm of every el-ementary operator coincide. We present an overview on some results of this flavour, in particular on recent extensions of the latter two results to antiliminal-by-abelian C*-algebras (obtained by Archbold, Somerset, and the author), and strong rigidity properties of the norm of elemen-tary operators on Calkin algebras due to Saksman and Tylli. 1. |
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The Pennsylvania State University CiteSeerX Archives |
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Text |
author |
Martin Mathieu |
spellingShingle |
Martin Mathieu Elementary operators on Calkin algebras |
author_facet |
Martin Mathieu |
author_sort |
Martin Mathieu |
title |
Elementary operators on Calkin algebras |
title_short |
Elementary operators on Calkin algebras |
title_full |
Elementary operators on Calkin algebras |
title_fullStr |
Elementary operators on Calkin algebras |
title_full_unstemmed |
Elementary operators on Calkin algebras |
title_sort |
elementary operators on calkin algebras |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.595.9135 http://www.maths.tcd.ie/pub/ims/bull46/S4602.pdf |
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ENVELOPE(24.117,24.117,65.717,65.717) |
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Klaus |
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Klaus |
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tylli |
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tylli |
op_source |
http://www.maths.tcd.ie/pub/ims/bull46/S4602.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.595.9135 http://www.maths.tcd.ie/pub/ims/bull46/S4602.pdf |
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766230866441273344 |