Polynomially accretive operators

Year 2024, Early Access, 1 - 12

Hranislav Stanković

https://doi.org/10.15672/hujms.1421159

Abstract

In this paper, we introduce a new class of operators on a complex Hilbert space $\mathcal{H}$ which is called polynomially accretive operators, and thereby extending the notion of accretive and $n$--real power positive operators. We give several properties of the newly introduced class, and generalize some results for accretive operators. We also prove that every $2$--normal and $(2k+1)$--real power positive operator, for some $k\in\mathbb{N}$, must be $n$--normal for all $n\geq2$. Finally, we give sufficient conditions for the normality in the preceding implication.

Keywords

polynomially accretive operators, accretive operators, $n$--real power positive operators, polynomially normal operators

References

• [1] S. A. Aluzuraiqi and A. B. Patel, On of n–normal operators, General Math Notes. 1, 61–73, 2010.