scholarly journals Additive mappings that preserve rank one nilpotent operators

2003 ◽  
Vol 367 ◽  
pp. 213-224 ◽  
Author(s):  
Wu Jing ◽  
Pengtong Li ◽  
Shijie Lu
Keyword(s):  
Nilpotent Operators ◽  
Rank One ◽  
Additive Mappings

Distance From Projections to Nilpotents

1995 ◽  
Vol 47 (4) ◽  
pp. 841-851 ◽  
Author(s):  
Gordon W. Macdonald
Keyword(s):  
Operator Norm ◽  
Arbitrary Rank ◽  
Shortest Distance ◽  
Nilpotent Operators ◽  
Rank One

AbstractThe 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 .

scholarly journals Additive mappings preserving operators of rank one

1993 ◽  
Vol 182 ◽  
pp. 239-256 ◽  
Author(s):  
Matjaž Omladič ◽  
Peter Šemrl
Keyword(s):  
Rank One ◽  
Additive Mappings

scholarly journals Additive mappings decreasing rank one

2002 ◽  
Vol 348 (1-3) ◽  
pp. 175-187 ◽  
Author(s):  
Bojan Kuzma
Keyword(s):  
Rank One ◽  
Additive Mappings

scholarly journals The Distance from a Rank Projection to the Nilpotent Operators on

2020 ◽  
pp. 1-21
Author(s):  
Zachary Cramer
Keyword(s):  
Minimal Distance ◽  
Nilpotent Operators ◽  
Rank One

Abstract Building on MacDonald’s formula for the distance from a rank-one projection to the set of nilpotents in $\mathbb {M}_n(\mathbb {C})$ , we prove that the distance from a rank $n-1$ projection to the set of nilpotents in $\mathbb {M}_n(\mathbb {C})$ is $\frac {1}{2}\sec (\frac {\pi }{\frac {n}{n-1}+2} )$ . For each $n\geq 2$ , we construct examples of pairs $(Q,T)$ where Q is a projection of rank $n-1$ and $T\in \mathbb {M}_n(\mathbb {C})$ is a nilpotent of minimal distance to Q. Furthermore, we prove that any two such pairs are unitarily equivalent. We end by discussing possible extensions of these results in the case of projections of intermediate ranks.

On Traces of n-Additive Mappings on Semiprime Ring

2017 ◽  
Vol 4 (1) ◽  
pp. 1-10
Author(s):  
Najat Muthana ◽  
◽  
Asma Ali ◽  
Kapil Kumar
Keyword(s):  
Semiprime Ring ◽  
Additive Mappings

Derivation of the Wave and Scattering Operators for an Interaction of Rank One

1970 ◽  
Vol 11 (8) ◽  
pp. 2415-2424 ◽  
Author(s):  
M. Anthea Grubb ◽  
D. B. Pearson
Keyword(s):  
Rank One ◽  
Scattering Operators

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

Sign in / Sign up

Export Citation Format

Share Document