Karpatsʹkì Matematičnì Publìkacìï (Jun 2023)

Applications of uniform boundedness principle to matrix transformations

  • M.A. Sarıgöl

DOI
https://doi.org/10.15330/cmp.15.1.236-245
Journal volume & issue
Vol. 15, no. 1
pp. 236 – 245

Abstract

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Using the uniform boundedness principle of Maddox, we characterize matrix transformations from the space $(\ell_{p}) _{T}$ to the spaces $m(\phi )$ and $n(\phi )$ for the case $1\leq p\leq \infty$, which correspond to bounded linear operators. Here $(\ell _{p})_{T}$ is the domain of an arbitrary triangle matrix $T$ in the space $\ell _{p}$, and the spaces $m(\phi )$ and $n(\phi )$ 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.

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