On the generalized Fuglede-Putnam theorem

M. H M Rashid, Mohd. Salmi Md. Noorani, A. S. Saari

Research output: Contribution to journalArticle

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(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*.

Original languageEnglish
Pages (from-to)239-246
Number of pages8
JournalTamkang Journal of Mathematics
Volume39
Issue number3
Publication statusPublished - 2008

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Keywords

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

ASJC Scopus subject areas

  • Metals and Alloys
  • Materials Science(all)

Cite this

Rashid, M. H. M., Md. Noorani, M. S., & Saari, A. S. (2008). On the generalized Fuglede-Putnam theorem. 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.

In: Tamkang Journal of Mathematics, Vol. 39, No. 3, 2008, p. 239-246.

Research output: Contribution to journalArticle

Rashid, MHM, Md. Noorani, MS & Saari, AS 2008, 'On the generalized Fuglede-Putnam theorem', Tamkang Journal of Mathematics, vol. 39, no. 3, pp. 239-246.
Rashid, M. H M ; Md. Noorani, Mohd. Salmi ; Saari, A. S. / On the generalized Fuglede-Putnam theorem. In: Tamkang Journal of Mathematics. 2008 ; Vol. 39, No. 3. pp. 239-246.
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