TY - GEN
A1 - Matkowski, Janusz
PB - Publishing House of Poznan University of Technology
N2 - The real functions satisfying the inequality Ф (uv) ≤ KФ (u) Ф (v) for some positive K which occur among others in [5], [3], [4], and referred there as submultiplicative, are discussed. A simplifying remark that Ф satisfies this inequality iff KФ is submultiplicative in the standard sense, is done. It is shown that, under general conditions, the standard submultiplicativity of Ф and the inequality Ф (u) Ф (1/u) ≤ 1 imply that Ф must be multi-plicative. Applying a result of Bhatt [1], we observe that if p is a nontrivial seminorm on a Banach algebra X such that the set { [formula] .. : ∈ G X, p (x) ≠ 0} is a singleton {λ}, then s = λp is a submultiplicative seminorm on X.
L1 - http://repozytorium.put.poznan.pl/Content/488960/Matkowski_Janusz_Remarks_on_submultiplicative_functions.pdf
L2 - http://repozytorium.put.poznan.pl/Content/488960
KW - submultiplicativitive function
KW - seminorm
KW - Orlicz function
KW - square property
T1 - Remarks on submultiplicative functions
UR - http://repozytorium.put.poznan.pl/dlibra/docmetadata?id=488960
ER -