SPECTRAL CONTINUITY OF (p,k)-QUASIPOSINORMAL
OPERATOR AND (p,k)-QUASIHYPONORMAL OPERATOR
D. Senthil Kumar1, D. Kiruthika2
1,2Post Graduate and Research Department of Mathematics
Government Arts College
Coimbatore, 641 018, Tamil Nadu, INDIA
Abstract. An operator $T \in B\mathcal{\mathcal{(H)}}$ is said to be $(p,k)$-quasiposinormal operator, if $T^{*k}(c^{2}(T^{*} T)^{p}-(T T^{*})^{p})T^{k} \geq 0$ for a positive integer $0 < p \leq 1$, some $c > 0$ and a positive integer $k$. In this paper, we prove that, the $(p,k)$ quasi-posinormal operator is a pole of resolvent of $T^{*}$. Then we prove that if $\{T_{n}\}$ is a sequence of operators in the class $(p, k) - \mathcal{Q}$ and $(p, k) - \mathcal{Q} \mathcal{P}$ which converges in the operator norm topology to an operator $T$ in the same class, then the functions spectrum, Weyl spectrum, Browder spectrum and essential surjectivity spectrum are continuous at $T$.
AMS Subject classification: 47A05, 47A10, 47B37
Keywords and phrases: Weyl's theorem, $(p,k)$-quasiposinormal operator, Riesz idempotent, generalized a-Weyl's theorem, B-Fredholm, B-Weyl


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DOI: 10.12732/ijam.v26i5.5

Volume: 26
Issue: 5
Year: 2013