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Distance From Projections to Nilpotents

Published online by Cambridge University Press:  20 November 2018

Gordon W. Macdonald
Gordon W. Macdonald*
Affiliation:
Department of Mathematics and Computer Science, University of Prince Edward Island, Charlottetown, Prince Edward Island, CIA 4P3
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Abstract

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The distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .

Keywords

47A5815A99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 4 , 01 August 1995 , pp. 841 - 851
Copyright
Copyright © Canadian Mathematical Society 1995

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