On the universal convergence sets

On existence of finite universal Korovkin sets in the centre of group algebras

“…Universal Korovkin closure and universal Korovkin sets w.r.t, positive contraction operators have been extensively investigated, see for example [3], [23], [24] and [25]. Unless otherwise specified, the phrase 'universal Korovkin set' will mean 'universal Korovkin set w.r.t, positive operators'.…”

“…For x~A, 2 and II II | denote respectively the Gelfand transform and the spectral radius of x. We adopt the definition of positivity and other notations as in ALXOMARE [3]. For the definition of an extendable positive linear functional on A and relevant properties, we refer to [16, w 24 H].…”

“…For the definition of universal Korovkin closure and universal Korovkin sets w.r.t, various classes of operators see [2], [3] and [4]. Universal Korovkin closure and universal Korovkin sets w.r.t, positive contraction operators have been extensively investigated, see for example [3], [23], [24] and [25].…”

“…Study of universal Korovkin sets in commutative Banach algebras with respect to various classes of operators was initiated by ALTOMARE [2,3,4]. Further investigations in different contexts have been carried out by PANNENBERG [20,21,22,23,24], BECKHOFF [7], ROMANELLI [26,27], and many others.…”

“…For equivalent definitions and more background on the subject the reader is referred to ALTOMARE [1,2,3,4], BAUER [5], BAUER and DONNER [6], BECKHOFF [7], PANNENBERG [20,21,22,23,24], PANNENBERG and ROMANELLI [25] and ROMANELLI [27].…”