Geodesic
Banach Spaces with the PC Property
Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 568-577

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A Banach space $X$ possesses the PC (point of continuity) property if for any $w$-closed bounded subset $A\subset X$ the identity map $(A,w)\to(A,\|\cdot\|)$ has a point of continuity ($w$ is the weak topology in $X$). We deduce some criteria for Banach spaces to have the PC property and describe (for dual Banach spaces) relationships between spaces possessing the PC property and spaces possessing the RN or the WRN property. 
@article{MZM_2004_76_4_a8,
     author = {V. I. Rybakov},
     title = {Banach {Spaces} with the {PC} {Property}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {568--577},
     publisher = {mathdoc},
     volume = {76},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a8/}
}
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V. I. Rybakov. Banach Spaces with the PC Property. Matematičeskie zametki, Tome 76 (2004) no. 4, pp. 568-577. http://geodesic.mathdoc.fr/item/MZM_2004_76_4_a8/