### Abstract

We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on ℬ(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 nonincreasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals.

Original language | English |
---|---|

Pages (from-to) | 253-266 |

Number of pages | 14 |

Journal | Linear Algebra and Its Applications |

Volume | 280 |

Issue number | 2-3 |

Publication status | Published - Sep 4 1998 |

### Fingerprint

### Keywords

- *-Semigroup isomorphism
- Linear rank preserver
- Operator ideal

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis

### Cite this

*Linear Algebra and Its Applications*,

*280*(2-3), 253-266.

**Linear rank and corank preserving maps on ℬ(H) and an application to *-semigroup isomorphisms of operator ideals.** / Györy, Máté; Molnár, L.; Šemrl, Peter.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 280, no. 2-3, pp. 253-266.

}

TY - JOUR

T1 - Linear rank and corank preserving maps on ℬ(H) and an application to *-semigroup isomorphisms of operator ideals

AU - Györy, Máté

AU - Molnár, L.

AU - Šemrl, Peter

PY - 1998/9/4

Y1 - 1998/9/4

N2 - We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on ℬ(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 nonincreasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals.

AB - We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on ℬ(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 nonincreasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals.

KW - -Semigroup isomorphism

KW - Linear rank preserver

KW - Operator ideal

UR - http://www.scopus.com/inward/record.url?scp=0039435554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039435554&partnerID=8YFLogxK

M3 - Article

VL - 280

SP - 253

EP - 266

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 2-3

ER -