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A note on range-kernel uncomplementation

Kubrusly C., Duggal B. P.

Demonstratio Mathematica

2017

Vol. 50, nr 1

252--260

This note exhibits a Banach-space operator such that neither the range nor the kernel is complemented both for the operator and its adjoint.

Weyl's theorems in the class of algebraically p-hyponormal operators

Duggal B. P., Djordjevic S. V.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2000

[Z] 40

49-56

An operator A, on an infinite dimensional complex Hilbert space H into itself, is said to be algebraically p-hyponormal, 0 < p SC 1, if there exists a polynomial q such that q(A) is p-hyponormal. In this paper we show that Weyl's theorems hold in the class of all algebraically p-hyponormal operators.