# Weyl Type Theorems for Unbounded Hyponormal Operators

• GUPTA, ANURADHA (Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi) ;
• MAMTANI, KARUNA (Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi)
• Received : 2014.10.02
• Accepted : 2015.02.21
• Published : 2015.09.23
• 52 28

#### Abstract

If T is an unbounded hyponormal operator on an infinite dimensional complex Hilbert space H with ${\rho}(T){\neq}{\phi}$, then it is shown that T satisfies Weyl's theorem, generalized Weyl's theorem, Browder's theorem and generalized Browder's theorem. The equivalence of generalized Weyl's theorem with generalized Browder's theorem, property (gw) with property (gb) and property (w) with property (b) have also been established. It is also shown that a-Browder's theorem holds for T as well as its adjoint $T^*$.

#### Keywords

Unbounded hyponormal operators;Weyl-type theorems;property (w);property (b)

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#### Cited by

1. Weyl type theorems for unbounded class- $$\mathcal {A}$$ A operators vol.28, pp.5-6, 2017, https://doi.org/10.1007/s13370-017-0479-7