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On the kernel space for an L 0 ‐linear function
Author(s) -
Zhang Xia,
Wang BaoZheng,
Liu Ming
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5296
Subject(s) - mathematics , normed vector space , kernel (algebra) , function space , normed algebra , space (punctuation) , generalization , combinatorics , continuous linear operator , discrete mathematics , real valued function , stratification (seeds) , pure mathematics , algebra over a field , mathematical analysis , seed dormancy , current algebra , linguistics , philosophy , botany , germination , dormancy , jordan algebra , biology
A random normed module is a random generalization of an ordinary normed space, and it is the randomization that makes a random normed module possess rich stratification structures. On the basis of these stratification structures, this paper shows that either the kernel space N ( f ) for an L 0 ‐linear function f from a random normed module S to the algebra L 0 ( F , K ) is a closed submodule or N ( f ) on some specifical stratification is a dense proper submodule of S , which generalizes the classical case. In the meantime, a characterization for the kernel space N ( f ) to be closed is also given.
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