Banach spaces l(p) (BC(N)) with the *- norm (parallel to)double over dot . (parallel to)double over dot(2,lp(BC(N))) and some properties

Sager N., Sağır Duyar B.

TBILISI MATHEMATICAL JOURNAL, vol.14, no.2, pp.65-81, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.32513/tmj/19322008123
  • Journal Name: TBILISI MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.65-81
  • Keywords: *-calculus, *-bicomplex number, completeness, Minkowski's inequality
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this work, we construct vector spaces l(p) (BC(N)) of absolutely p- summable *-bicomplex sequences with the *-norm (parallel to)over double dot . (parallel to)over double dot(2,lp(BC(N))) over the field C(N). Also, we show that some inclusion relations hold and these vector spaces are Banach spaces by using Minkowski's inequality in BC(N) with respect to (parallel to)over double dot . (parallel to)over double dot(2).