Applications of uniform boundedness principle to matrix transformations - Sarıgöl, M.A. (Carpathian Mathematical Publications, 2023)
Using the uniform boundedness principle of Maddox, we characterize matrix transformations from the space (_p) _T to the spaces m(φ ) and n(φ ) for the case 1≤ p≤ ∞, which correspond to bounded linear operators. Here (_p)_T is the domain of an arbitrary triangle matrix T in the space _p, and the spaces m(φ ) and n(φ ) are introduced by W.L.C. Sargent. In special cases, we get some well known results of W.L.C. Sargent, M. Stieglitz and H. Tietz, E. Malkowsky and E. Savaş. Also we give other applications including some important new classes.