@misc{10498/24891,
year = {2021},
month = {4},
url = {http://hdl.handle.net/10498/24891},
abstract = {This paper is on general methods of convergence and summability. We first present the general method of convergence described by free filters of N and study the space of convergence associated with the filter. We notice that c(X) is always a space of convergence associated with a filter (the Frechet filter); that if X is finite dimensional, then l infinity (X) is a space of convergence associated with any free ultrafilter of N; and that if X is not complete, then l infinity (X) is never the space of convergence associated with any free filter of N. Afterwards, we define a new general method of convergence inspired by the Banach limit convergence, that is, described through operators of norm 1 which are an extension of the limit operator. We prove that l infinity (X) is always a space of convergence through a certain class of such operators; that if X is reflexive and 1-injective, then c(X) is a space of convergence through a certain class of such operators; and that if X is not complete, then c(X) is never the space of convergence through any class of such operators. In the meantime, we study the geometric structure of the set HB(lim):={T is an element of B(l infinity (X),X):T|c(X)=lim and parallel to T parallel to =1} and prove that HB(lim) is a face of BLX0</mml:msubsup> if X has the Bade property, where LX0</mml:msubsup>:={T is an element of B(<mml:msub>l infinity (X),X):<mml:msub>c0(X)subset of ker(T)}. Finally, we study the multipliers associated with series for the above methods of convergence.},
publisher = {SPRINGER},
keywords = {Methods},
keywords = {Convergence},
keywords = {Summability},
keywords = {47A05},
title = {General methods of convergence and summability},
doi = {10.1186/s13660-021-02587-x},
author = {García Pacheco, Francisco Javier and Kama, Ramazan and Listán García, María del Carmen},
}