| Title:
|
A study on best approximation and Banach algebra in $n$-normed linear space (English) |
| Author:
|
Ghosh, Prasenjit |
| Author:
|
Samanta, Tapas Kumar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
3 |
| Year:
|
2026 |
| Pages:
|
449-479 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The idea of best approximation in linear $n$-normed space is presented and some examples showing various possibilities of best approximations in linear $n$-normed space is given. Also, we study strictly convex $n$-norm and enquire about the uniqueness of best approximations in $n$-normed linear space. Furthermore, best approximations in $n$-Hilbert space is discussed. Moreover, the notion of a Banach algebra in $n$-Banach space is presented and some examples are discussed. A set-theoretic property of invertible and noninvertible elements in an $n$-Banach algebra is explained and then topological divisor of zero in $n$-Banach algebra is defined. Finally, we introduce the notion of a complex homeomorphism in an $n$-Banach algebra and derive Gleason, Kahane, Zelazko type theorem with the help of complex $b$-homeomorphism in the case of $n$-Banach algebra. (English) |
| Keyword:
|
$n$-normed space |
| Keyword:
|
$n$-Banach space |
| Keyword:
|
$b$-linear functional |
| Keyword:
|
Banach algebra |
| Keyword:
|
complex homeomorphism |
| MSC:
|
46A22 |
| MSC:
|
46B07 |
| MSC:
|
46B25 |
| DOI:
|
10.21136/MB.2025.0159-24 |
| . |
| Date available:
|
2026-08-24T07:52:45Z |
| Last updated:
|
2026-08-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153717 |
| . |
| Reference:
|
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