Abstract
Abstract The author has computed the bounds of the Hilbert operator on some sequence spaces [18, 19]. Through this study the author has investigated the bounds of operators on the Hilbert sequence space and the present study is a complement of those previous research.
Highlights
Let p ≥ and ω denote the set of all real-valued sequences
Through this study the author has investigated the bounds of operators on the Hilbert sequence space and the present study is a complement of those previous research
The operator T is called bounded, if the inequality Tx p ≤ K x p holds for all sequences x ∈ p, while the constant K is not depending on x
Summary
Let p ≥ and ω denote the set of all real-valued sequences. The space p is the set of all real sequences x = (xk) ∈ ω such that. The operator T is called bounded, if the inequality Tx p ≤ K x p holds for all sequences x ∈ p, while the constant K is not depending on x. The constant K is called an upper bound for operator T and the smallest possible value of K is called the norm of T. The lower bound of T is the greatest possible value of L. The matrix domain of an in nite matrix A in a sequence space X is de ned as A(X) =. By using matrix domains of special triangle matrices in classical spaces, many authors have introduced and studied new Banach spaces
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
