### Abstract

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got used to when dealing with linear preserver problems, hence we restrict our attention to certain important classes of operators like idempotents, or projections, or partial isometries. We conclude the paper with a result on the form of linear maps which preserve the left ideals in B(H).

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

Pages (from-to) | 311-321 |

Number of pages | 11 |

Journal | Linear Algebra and Its Applications |

Volume | 286 |

Issue number | 1-3 |

Publication status | Published - Jan 1 1999 |

### Fingerprint

### Keywords

- Idempotents
- Linear preservers
- One-sided ideals
- Partial isometries
- Projections

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis

### Cite this

*Linear Algebra and Its Applications*,

*286*(1-3), 311-321.

**Some linear preserver problems on B(H) concerning rank and corank.** / Molnár, L.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 286, no. 1-3, pp. 311-321.

}

TY - JOUR

T1 - Some linear preserver problems on B(H) concerning rank and corank

AU - Molnár, L.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got used to when dealing with linear preserver problems, hence we restrict our attention to certain important classes of operators like idempotents, or projections, or partial isometries. We conclude the paper with a result on the form of linear maps which preserve the left ideals in B(H).

AB - As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got used to when dealing with linear preserver problems, hence we restrict our attention to certain important classes of operators like idempotents, or projections, or partial isometries. We conclude the paper with a result on the form of linear maps which preserve the left ideals in B(H).

KW - Idempotents

KW - Linear preservers

KW - One-sided ideals

KW - Partial isometries

KW - Projections

UR - http://www.scopus.com/inward/record.url?scp=0040814343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040814343&partnerID=8YFLogxK

M3 - Article

VL - 286

SP - 311

EP - 321

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -