Annals of Functional Analysis

Weyl type theorems for algebraically Quasi-$\mathcal{HNP}$ operators

T. Prasad and M. H. M. Rashid

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper, by introducing the class of quasi hereditarily normaloid polaroid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations $f(T + A)$, where $A$ is algebraic and commutes with $T,$ and $f$ is an analytic function, defined on an open neighborhood of the spectrum of $T +A$, such that $f$ is non constant on each of the components of its domain.

Article information

Ann. Funct. Anal., Volume 6, Number 3 (2015), 262-274.

First available in Project Euclid: 17 April 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A10: Spectrum, resolvent
Secondary: 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]

Hereditarily normaloid polaroid operator polaroid operator Weyl type theorem


Rashid, M. H. M.; Prasad, T. Weyl type theorems for algebraically Quasi-$\mathcal{HNP}$ operators. Ann. Funct. Anal. 6 (2015), no. 3, 262--274. doi:10.15352/afa/06-3-19.

Export citation


  • P. Aiena, "Fredhlom and Local Specral Theory with Application to Multipliers", Kluwer Acad. Publishers, Dordrecht, 2004.
  • P. Aiena, J.R. Guillen and P. Peña, A Unifying approch to Weyl Type Theorems for Banach Space operators, Integral Equations Operator Theory 77 (2013),371–384.
  • P. Aiena, Algebraically paranormal operators on Banach spaces, Banach J. Math. Anal. 7 (2013), no. 2, 136–145.
  • M. Amouch and H. Zguitti, On the equivalence of Browder's and generalized Browder's theorem, Glasg. Math. J. 48 (2006), 179–185.
  • M. Berkani and J.J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003) 359–376.
  • M. Berkani, On the equivalence of Weyl's theorem and generalized Weyl's theorem, Acta Math. Sin. 272 (2007) 103–110.
  • M. Berkani, B-Weyl spectrum and poles of the resolvant, J. Math. Anal. Appl. 272 (2002), 596–603.
  • M. Berkani and J. Koliha, Weyl Type theorems for bounded linear operators, Acta. Sci. Math. (Szeged) 69 (2003), 359–376.
  • L.A. Coburn, Weyl's theorem for non-normal operators, Michigan Math. J. 13 (1966), 285–288.
  • B.P. Duggal, I.H. Jeon and I.H. Kim, On Weyl's theorem for quasi-class $A$ operators, J. Korean Math. Soc. 43 (2006), no. 4, 899-909.
  • B.P. Duggal, Hereditarily polaroid operators, SVEP and Weyls theorem, J. Math. Anal. Appl. 340 (2008), 366–373.
  • B.P. Duggal and S.V. Djordjevic, Generalized Weyl's theorem for a class of operators satisfying a norm condition, Mathematical Proceedings of the Royal Irish Academy 104 A (2004), 75–81.
  • B.P. Duggal, Perturbations and Weyl's theorem, Proc. Amer. Math. Soc. 135 (2007), 2899–2905.
  • W.Y. Lee, Weyl's spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), 131–138.
  • S. Mecheri, Bishop's property $(\beta)$ and Riesz idempotent for k-quasi-paranormal operators, Banach J. Math. Anal. 6 (2012), 147–154.
  • M. Oudghiri, Weyl's and Browder's theorem for operators satisfying the SVEP, Studia Math. 163 (2004), 85–101.
  • V. Rakočević, Operators obeying a-Weyl's theorem, Rev. Roumaine Math. Pures Appl. 10 (1986), 915–919.
  • M.H.M. Rashid and M.S.M. Noorani, Weyl's type theorems for algebraically $w$-hyponormal operators, Arab. J. Sci. Eng. 35 (2010),103–116.
  • M.H.M. Rashid, Property $(w)$ and quasi-class $(A,k)$ operators, Revista De Le Unión Math. Argentina 52 (2011), 133–142.
  • M.H.M. Rashid and M.S.M. Noorani, Weyl's type theorems for algebraically $(p,k)$-quasihyponormal operators, Commun. Korean Math. Soc. 27 (2012), 77–95.
  • J.T. Yuan and G.X. Ji, On $(n, k)$-quasi paranormal operators, Studia Math. 209 (2012), 289–301.