N-NORMED SPACES WITH RESPECT TO ITS QUOTIENT SPACES
The concept of n-normed spaces, for n 2 is a generalization of the concept of normed spaces. The structure of n-normed spaces has been studied since S. G¨ahler introduced the concept on 1960’s. This disertation contains some results about charactheristics of n-normed spaces with respect to norms...
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| Format: | Dissertations |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/51053 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The concept of n-normed spaces, for n 2 is a generalization of the concept
of normed spaces. The structure of n-normed spaces has been studied since S.
G¨ahler introduced the concept on 1960’s. This disertation contains some results
about charactheristics of n-normed spaces with respect to norms that is derived
from n-norm on its quotient spaces. These norms will be a new viewpoint to
investigate some characterisics of n-normed spaces. Some topological properties
of the n-normed spaces haas been studied in this research. Moreover, the number
of norms that are used to investigate the topological properties become one of
our concern. Therefore, we give a condition to minimize the number of norms
that can be used to investigate the properties. We use the norms on the quotient
spaces to study continuous and contractive functions in n-normed spaces. By using
some properties that has been studied earlier, we proved Fixed Point Theorem of
contractive mappings on closed and bounded sets in the n-normed spaces. We
also proved Fixed Point Theorem on p-summable sequence space (`p) as one of
n-normed spaces. In the end of this disertation, this research focused on bounded
linear functionals and bounded k-linear functionals with their dual spaces respectively. |
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