Abstract
Let be the Euclidean spectral radius associated with a q-tuple of bounded linear operators on a complex Hilbert space. The principal objective of our study is to establish various compelling upper bounds involving . In particular, our findings demonstrate that, for all , we have Here, represents the generalized spherical Aluthge transform of , while the notations , , and pertain to the joint numerical radius, joint operator norm, and Euclidean operator norm, respectively, of operators in Hilbert spaces. Furthermore, we extend the notions of spherical and Duggal transforms and derive multiple upper bounds for in relation to these transforms. Additionally, there are some applications that are derived as well.
Acknowledgments
The authors want to thank the referees for their helpful comments and for reading the original manuscript carefully. Their comments made the final version better. The first author wants to thank the Distinguished Scientist Fellowship Program at King Saud University in Saudi Arabia for providing funding for this project through Researchers Supporting Project number (RSP2024R187).
Disclosure statement
No potential conflict of interest was reported by the author(s).