<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
                     <mfenced open="(" close=")" separators="|">
                        <mrow>
                           <mi>α</mi>
                           <mo>,</mo>
                           <mi>β</mi>
                        </mrow>
                     </mfenced>
                  </math>-Normal Operators in Several Variables

<p>In this paper, we aim to investigate the class of jointly hyponormal operators related to a positive operator $ A $ on a complex Hilbert space $ \mathcal{X} $, which is called jointly $ A $-hyponormal. This notion was first introduced by Guesba et al. in [Linear and Multilinear Algebra, 69(15), 2888–2907] for $ m $-tuples of operators that admit adjoint operators with respect to $ A $. Mainly, we prove that if $ \mathbf{B} = (B_1, \cdots, B_m) $ is a jointly $ A $-hyponormal $ m $-tuple of commuting operators, then $ \mathbf{B} $ is jointly $ A $-normaloid. This result allows us to establish, for a particular case when $ A $ is the identity operator, a sharp bound for the distance between two jointly hyponormal $ m $-tuples of operators, expressed in terms of the difference between their Taylor spectra. We also aim to introduce and investigate the class of spherically $ A $-$ p $-hyponormal operators with $ 0 < p < 1 $. Additionally, we study the tensor product of specific classes of multivariable operators in semi-Hilbert spaces.</p>

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

$(α, β)$ -Normal Operators in Several Variables

Abstract: We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality, and quasi-hyponormalit… Show more

Cited by 2 publications

References 20 publications

On A -normaloid d -tuples of operators and related questions

On A -normaloid d -tuples of operators and related questions

Jointly $ A $-hyponormal $ m $-tuple of commuting operators and related results

Contact Info

Product

Resources

About

α , β -Normal Operators in Several Variables

Abstract: We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality, and quasi-hyponormalit… Show more

Cited by 2 publications

References 20 publications

On A -normaloid d -tuples of operators and related questions

On A -normaloid d -tuples of operators and related questions

Jointly $ A $-hyponormal $ m $-tuple of commuting operators and related results

Contact Info

Product

Resources

About

$(α, β)$ -Normal Operators in Several Variables