Open Access

The Fuglede-Putnam theorem for -quasihyponormal operators

Journal of Inequalities and Applications20062006:47481

DOI: 10.1155/JIA/2006/47481

Received: 8 September 2004

Accepted: 19 September 2004

Published: 22 January 2006


We show that if is a -quasihyponormal operator and is a -hyponormal operator, and if , where is a quasiaffinity (i.e., a one-one map having dense range), then is a normal and moreover is unitarily equivalent to .


Authors’ Affiliations

Department of Mathematics, Seoul National University


  1. Aluthge A: On-hyponormal operators for. Integral Equations and Operator Theory 1990,13(3):307–315. 10.1007/BF01199886MATHMathSciNetView ArticleGoogle Scholar
  2. Arora SC, Arora P: On-quasihyponormal operators for. Yokohama Mathematical Journal 1993,41(1):25–29.MATHMathSciNetGoogle Scholar
  3. Campbell SL, Gupta BC: On-quasihyponormal operators. Mathematica Japonica 1978/1979,23(2):185–189.MathSciNetMATHGoogle Scholar
  4. Chō M, Itoh M: Putnam's inequality for-hyponormal operators. Proceedings of the American Mathematical Society 1995,123(8):2435–2440.MATHMathSciNetGoogle Scholar
  5. Duggal BP: On-quasihyponormal operators for. Yokohama Mathematical Journal 1993, 41: 25–29.MathSciNetGoogle Scholar
  6. Gupta BC, Ramanujan PB: On-quasihyponormal operators II. The Tohoku Mathematical Journal 1968, 20: 417–424. 10.2748/tmj/1178243070View ArticleMATHGoogle Scholar
  7. Jeon IH, Duggal BP: -hyponormal operators and quasisimilarity. Integral Equations and Operator Theory 2004,49(3):397–403. 10.1007/s00020-002-1210-zMATHMathSciNetView ArticleGoogle Scholar
  8. Kim IH: On-quasihyponormal operators. Mathematical Inequalities & Applications 2004,7(4):629–638.MATHMathSciNetView ArticleGoogle Scholar
  9. Sheth IH: On hyponormal operators. Proceedings of the American Mathematical Society 1966, 17: 998–1000. 10.1090/S0002-9939-1966-0196498-7MATHMathSciNetView ArticleGoogle Scholar
  10. Stampfli JG, Wadhwa BL: An asymmetric Putnam-Fuglede theorem for dominant operators. Indiana University Mathematics Journal 1976,25(4):359–365. 10.1512/iumj.1976.25.25031MATHMathSciNetView ArticleGoogle Scholar
  11. Tanahashi K, Uchiyama A, Chō M: Isolated points of spectrum of-quasihyponormal operators. Linear Algebra and its Applications 2004, 382: 221–229.MATHMathSciNetView ArticleGoogle Scholar
  12. Uchiyama A: An example of a-quasihyponormal operato. Yokohama Mathematical Journal 1999,46(2):179–180.MATHMathSciNetGoogle Scholar
  13. Williams JP: Operators similar to their adjoints. Proceedings of the American Mathematical Society 1969, 20: 121–123. 10.1090/S0002-9939-1969-0233230-5MATHMathSciNetView ArticleGoogle Scholar


© Hindawi Publishing Corporation. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.