Abstract
In this paper, we aim to develop formulas of spectral radius for an operator S in terms of generalized Aluthge transform, numerical radius, iterated generalized Aluthge transform, and asymptotic behavior of powers of S . These formulas generalize some of the formulas of spectral radius existing in literature. As an application, these formulas are used to obtain several characterizations of normaloid operators.
Highlights
In mathematical analysis and in functional analysis, the spectral analysis of operators is an essential research topic
The spectrum of an operator is connected with an invariant subspace problem on a complex Hilbert space, and the important property of spectrum is the expression of spectral radius in various formulas
An operator can be decomposed into two Hermitian operators being its real and imaginary parts, and this decomposition is known as Cartesian decomposition
Summary
In mathematical analysis and in functional analysis, the spectral analysis of operators is an essential research topic. The spectrum of an operator is connected with an invariant subspace problem on a complex Hilbert space (see [2]), and the important property of spectrum is the expression of spectral radius in various formulas (see [3–5]). In [13], Aluthge introduced a transform to study the properties of hyponormal operators that were connected with the invariant subspace problem in operator theory This transform is called Aluthge transform, which is defined as. Chabbabi and Mbekhta [12] gave various expressions for spectral radius formulas involving λ-Aluthge transform, iterated λ-Aluthge transform, asymptotic behavior of powers of an operator, and numerical radius.
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