Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 16 5 2025 05 01 A new generalization of the $l_p$ spaces 165 172 8897 10.22075/ijnaa.2023.27002.3472 EN Alireza Moazzen Department of Mathematics, Kosar University of Bojnord, Bojnord, Iran Journal Article 2022 05 23 In this work, using semidefinite matrices gives a new generalization of the $l_p$ spaces and some inequalities containing lower bounds of some operators are proved. Also, by defining an inner product on the classes of an equivalence relation on operators, some inequalities similar to the well-known inequalities including the Copson, Cesaro, Hilbert and Hardy inequalities are obtained. Lower bound of operator Hilbert's operator Cesaro operator https://ijnaa.semnan.ac.ir/article_8897_d0e34f099f3dae4b1b4a9759580da6ab.pdf