Geodesic
Test closure operations in a~Banach space that are generated by linear functionals
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 25, Tome 247 (1997), pp. 114-145

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Some criteria are proved for an element of a Banach space to belong to a certain test or Korovkin closure of a given set. The operations of closure in question are determined by linear functionals. The cases of arbitrary linear functionals and of positive functionals are considered. Some sufficient conditions are given for a test closure to coincide with a Korovkin closure. 
@article{ZNSL_1997_247_a7,
     author = {L. G. Labsker},
     title = {Test closure operations in {a~Banach} space that are generated by linear functionals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--145},
     publisher = {mathdoc},
     volume = {247},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_247_a7/}
}
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L. G. Labsker. Test closure operations in a~Banach space that are generated by linear functionals. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 25, Tome 247 (1997), pp. 114-145. http://geodesic.mathdoc.fr/item/ZNSL_1997_247_a7/