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Inclusion Mappings between Orlicz Sequence Spaces

✍ Scribed by Lech Maligranda; Mieczysław Mastyło

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
148 KB
Volume
176
Category
Article
ISSN
0022-1236

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✦ Synopsis

It is shown that if l . is an Orlicz sequence space, then the space l w 1 (l . ) of weakly summable sequences in l . is continuously embedded into l . (l 2 ) (resp., into l . (l . )) whenever t [ .(-t) is equivalent to a concave function (resp., a convex function and . is a supermultiplicative function). By combining the above results with the interpolation theory we proved continuous inclusions between spaces l w 1 (l . 0 ) and l , (l . 1 ), where l . 0 / Ä l . 1 and , is a certain Orlicz function depending on . 0 and . 1 .

In particular, if . 0 and . 1 are power functions we obtain the well known result on (r, 1)-summability of the inclusion mappings between l p -spaces proved independently by G.

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