A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
1983 ◽
Vol 26
(1)
◽
pp. 118-120
◽
AbstractA Banach space is fully 2-rotund if (xn) converges whenever ‖xn + xm‖ converges as m, n → ∞ and locally uniformly rotund if xn → x whenever ‖xn‖ and ‖(xn + x)/2‖ → ‖x‖.We show that I2 with the equivalent normis fully 2-rotund but not locally uniformly rotund, thus answering in the negative a question first raised by Fan and Glicksberg in 1958.
Keyword(s):
1979 ◽
Vol 85
(2)
◽
pp. 317-324
◽
2000 ◽
Vol 43
(3)
◽
pp. 511-528
◽
Keyword(s):
1992 ◽
Vol 34
(1)
◽
pp. 1-9
◽
Keyword(s):
1971 ◽
Vol 23
(3)
◽
pp. 468-480
◽
1961 ◽
Vol 13
◽
pp. 505-518
◽
Keyword(s):
1980 ◽
Vol 32
(2)
◽
pp. 421-430
◽
Keyword(s):
1983 ◽
Vol 26
(3)
◽
pp. 353-360
◽
1976 ◽
Vol 19
(1)
◽
pp. 7-12
◽
Keyword(s):