### Abstract

In this paper, we prove the following assertions: (1) If the pair of operators (A, B*) satisfies the Fuglede-Putnam Property and S ∈ ker(δ_{A,B}), where S ∈ B(H), then we have ||δ_{A,B} X + S|| ≥ ||S||. (2) Suppose the pair of operators (A, B*) satisfies the Fuglede-Putnam Property. If A^{2}X = XB ^{2} and A^{3} X = XB^{3}, then AX = X B. (3) Let A, B ∈ B(H) be such that A, B* are p-hyponormal. Then for any X ∈ C_{2}, AX-XB ∈ C_{2} implies A* X - XB* ∈ C_{2}. (4) Let T, S ∈ B(H) be such that T and S* are quasihyponormal operators. If X ∈ B(H) and TX = XS, then T* X = XS*.

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

Pages (from-to) | 239-246 |

Number of pages | 8 |

Journal | Tamkang Journal of Mathematics |

Volume | 39 |

Issue number | 3 |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- Fuglede-Putnam theorem
- Hilbert schmidt operator
- Normal derivation
- p-hyponormal
- Quasihyponormal

### ASJC Scopus subject areas

- Metals and Alloys
- Materials Science(all)

### Cite this

*Tamkang Journal of Mathematics*,

*39*(3), 239-246.

**On the generalized Fuglede-Putnam theorem.** / Rashid, M. H M; Md. Noorani, Mohd. Salmi; Saari, A. S.

Research output: Contribution to journal › Article

*Tamkang Journal of Mathematics*, vol. 39, no. 3, pp. 239-246.

}

TY - JOUR

T1 - On the generalized Fuglede-Putnam theorem

AU - Rashid, M. H M

AU - Md. Noorani, Mohd. Salmi

AU - Saari, A. S.

PY - 2008

Y1 - 2008

N2 - In this paper, we prove the following assertions: (1) If the pair of operators (A, B*) satisfies the Fuglede-Putnam Property and S ∈ ker(δA,B), where S ∈ B(H), then we have ||δA,B X + S|| ≥ ||S||. (2) Suppose the pair of operators (A, B*) satisfies the Fuglede-Putnam Property. If A2X = XB 2 and A3 X = XB3, then AX = X B. (3) Let A, B ∈ B(H) be such that A, B* are p-hyponormal. Then for any X ∈ C2, AX-XB ∈ C2 implies A* X - XB* ∈ C2. (4) Let T, S ∈ B(H) be such that T and S* are quasihyponormal operators. If X ∈ B(H) and TX = XS, then T* X = XS*.

AB - In this paper, we prove the following assertions: (1) If the pair of operators (A, B*) satisfies the Fuglede-Putnam Property and S ∈ ker(δA,B), where S ∈ B(H), then we have ||δA,B X + S|| ≥ ||S||. (2) Suppose the pair of operators (A, B*) satisfies the Fuglede-Putnam Property. If A2X = XB 2 and A3 X = XB3, then AX = X B. (3) Let A, B ∈ B(H) be such that A, B* are p-hyponormal. Then for any X ∈ C2, AX-XB ∈ C2 implies A* X - XB* ∈ C2. (4) Let T, S ∈ B(H) be such that T and S* are quasihyponormal operators. If X ∈ B(H) and TX = XS, then T* X = XS*.

KW - Fuglede-Putnam theorem

KW - Hilbert schmidt operator

KW - Normal derivation

KW - p-hyponormal

KW - Quasihyponormal

UR - http://www.scopus.com/inward/record.url?scp=58449135763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58449135763&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:58449135763

VL - 39

SP - 239

EP - 246

JO - Tamkang Journal of Mathematics

JF - Tamkang Journal of Mathematics

SN - 0049-2930

IS - 3

ER -